Kay Brandner, Taro Hanazato, *Keiji Saito,

Thermodynamic Bounds on Precision in Ballistic Multi-Terminal Transport,

Physical Review Letters 120, 090601/1-5 (2018).

A01-002 KOBAYASHI

### Paper | Original Paper

#### 2018

Hiroki Taniguchi, Shota Suzuki, Tomonori Arakawa, Hiroyuki Yoshida, *Yasuhiro Niimi, and Kensuke Kobayashi,

Fabrication of thin films of two-dimensional triangular antiferromagnet Ag2CrO2 and their transport properties,

AIP Advances 8, 025010/1-6 (2018).

[Summary] We fabricated 100 nm thick films of two-dimensional triangular antiferromagnet Ag2CrO2 using the mechanical exfoliation technique, and performed the transport measurements down to 5 K. As in the case of polycrystalline samples, a large reduction of the resistivity due to the antiferromagnetic ordering was clearly observed at around 25 K. Surprisingly, the resistivity for the thin films is one order magnitude smaller than that for the polycrystalline samples, indicating that the crystalline nature is much better in the former than in the latter. The present result sheds new light on the use of atomic-layer antiferromagnetic materials for device applications.

#### 2017

Kazuya Kaneko, Eiki Iyoda, and Takahiro Sagawa,

Saturation of entropy production in quantum many-body systems,

Physical Review E 96, 062148/1-10 (2017).

[Summary] Bridging the second law of thermodynamics and microscopic reversible dynamics has been a longstanding problem in statistical physics. Here, we address this problem on the basis of quantum many-body physics, and discuss how the entropy production saturates in isolated quantum systems under unitary dynamics. First, we rigorously prove that the entropy production does indeed saturate in the long time regime, even when the total system is in a pure state. Second, we discuss the non-negativity of the entropy production at saturation, implying the second law of thermodynamics. This is based on the eigenstate thermalization hypothesis, which states that even a single energy eigenstate is thermal. We also numerically demonstrate that the entropy production saturates at a non-negative value even when the initial state of a heat bath is a single energy eigenstate. Our results reveal fundamental properties of the entropy production in isolated quantum systems at late times.

Shuji Tamaki, Makiko Sasada, and *Keiji Saito,

Heat Transport via Low-Dimensional Systems with Broken Time-Reversal Symmetry,

Physical Review Letters 119, 110602 (2017).

*Eiki Iyoda, Kazuya Kaneko, Takahiro Sagawa,,

Fluctuation Theorem for Many-Body Pure Quantum States,

Physical Review Letters 119, 100601/1-6 (2017).

[Summary] We prove the second law of thermodynamics and the nonequilibrium fluctuation theorem for pure quantum states. The entire system obeys reversible unitary dynamics, where the initial state of the heat bath is not the canonical distribution but is a single energy eigenstate that satisfies the eigenstate-thermalization hypothesis. Our result is mathematically rigorous and based on the Lieb-Robinson bound, which gives the upper bound of the velocity of information propagation in many-body quantum systems. The entanglement entropy of a subsystem is shown connected to thermodynamic heat, highlighting the foundation of the information-thermodynamics link. We confirmed our theory by numerical simulation of hard-core bosons, and observed dynamical crossover from thermal fluctuations to bare quantum fluctuations. Our result reveals a universal scenario that the second law emerges from quantum mechanics, and can be experimentally tested by artificial isolated quantum systems such as ultracold atoms.

*Yuma Fujimoto, Takahiro Sagawa, Kunihiko Kaneko,,

Hierarchical prisoner’s dilemma in hierarchical game for resource competition,

New Journal of Physics 19, 073008/1-12 (2017).

[Summary] Dilemmas in cooperation are one of the major concerns in game theory. In a public goods game, each individual cooperates by paying a cost or defecting without paying it, and receives a reward from the group out of the collected cost. Thus, defecting is beneficial for each individual, while cooperation is beneficial for the group. Now, groups (say, countries) consisting of individuals also play games. To study such a multi-level game, we introduce a hierarchical game in which multiple groups compete for limited resources by utilizing the collected cost in each group, where the power to appropriate resources increases with the population of the group. Analyzing this hierarchical game, we found a hierarchical prisoner's dilemma, in which groups choose the defecting policy (say, armament) as a Nash strategy to optimize each group's benefit, while cooperation optimizes the total benefit. On the other hand, for each individual, refusing to pay the cost (say, tax) is a Nash strategy, which turns out to be a cooperation policy for the group, thus leading to a hierarchical dilemma. Here the group reward increases with the group size. However, we find that there exists an optimal group size that maximizes the individual payoff. Furthermore, when the population asymmetry between two groups is large, the smaller group will choose a cooperation policy (say, disarmament) to avoid excessive response from the larger group, and the prisoner's dilemma between the groups is resolved. Accordingly, the relevance of this hierarchical game on policy selection in society and the optimal size of human or animal groups are discussed.

*Hiroki Yamaguchi, Kyogo Kawaguchi, Takahiro Sagawa,,

Dynamical crossover in a stochastic model of cell fate decision,

Phyical Review E 96, 012401/1-8 (2017).

[Summary] We study the asymptotic behaviors of stochastic cell fate decision between proliferation and differentiation. We propose a model of a self-replicating Langevin system, where cells choose their fate (i.e., proliferation or differentiation) depending on local cell density. Based on this model, we propose a scenario for multicellular organisms to maintain the density of cells (i.e., homeostasis) through finite-ranged cell-cell interactions. Furthermore, we numerically show that the distribution of the number of descendant cells changes over time, thus unifying the previously proposed two models regarding homeostasis: the critical birth death process and the voter model. Our results provide a general platform for the study of stochastic cell fate decision in terms of nonequilibrium statistical mechanics.

*Meydi Ferrier, Tomonori Arakawa, Tokuro Hata, Ryo Fujiwara, Raphaëlle Delagrange, Richard Deblock, Yoshimichi Teratani, Rui Sakano, Akira Oguri, *Kensuke Kobayashi,

Quantum fluctuations along symmetry crossover in a Kondo-correlated quantum dot,

Physical Review Letters 118, 196803/1-5 (2017).

[Summary] Universal properties of entangled many-body states are controlled by their symmetry and quantum fluctuations. By the magnetic-field tuning of the spin-orbital degeneracy in a Kondo-correlated quantum dot, we have modified quantum fluctuations to directly measure their influence on the many-body properties along the crossover from SU(4) to SU(2) symmetry of the ground state. High-sensitive current noise measurements combined with the nonequilibrium Fermi liquid theory clarify that the Kondo resonance and electron correlations are enhanced as the fluctuations, measured by the Wilson ratio, increase along the symmetry crossover. Our achievement demonstrates that nonlinear noise constitutes a measure of quantum fluctuations that can be used to tackle quantum phase transitions.

*Shuichi Iwakiri, Yasuhiro Niimi, Kensuke Kobayashi,

Dynamics of pure spin current in high-frequency quantum regime,

Applied Physics Express 10, 053001/1-4 (2017).

[Summary] Pure spin current is a powerful tool for manipulating spintronic devices, and its dynamical behavior is an important issue. By using the mesoscopic transport theory for electron tunneling induced by spin accumulation, we investigate the dynamics of the spin current in the high-frequency quantum regime, where the effect of frequency is much greater than those of temperature and bias voltage. Besides the thermal noise, frequency-dependent ﬁnite noise emerges, signaling the spin current across the tunneling barrier. We also ﬁnd that the autocorrelation of the spin current exhibits sinusoidal oscillation with time as a consequence of the Pauli exclusion principle even without any net charge current.

#### 2016

*Shumpei Yamamoto, Sosuke Ito, Naoto Shiraishi, and Takahiro Sagawa,

Linear irreversible thermodynamics and Onsager reciprocity for information-driven engines,

Phyical Review E 94, 052121/1-11 (2016).

[Summary] In the recent progress in nonequilibrium thermodynamics, information has been recognized as a kind of thermodynamic resource that can drive thermodynamic current without any direct energy injection. In this paper, we establish the framework of linear irreversible thermodynamics for a broad class of autonomous information processing. In particular, we prove that the Onsager reciprocity holds true with information: The linear response matrix is well-defined and is shown symmetric with both of the information affinity and the conventional thermodynamic affinity. As an application, we derive a universal bound for the efficiency at maximum power for information-driven engines in the linear regime. Our result reveals the fundamental role of information flow in linear irreversible thermodynamics.

Naoto Shiraishi, Keiji Saito and Hal Tasaki,

Universal trade-off relation between power and efficiency for heat engines,

Physical Review Letters 117, 190601/1-5 (2016).

[Summary] For a general thermodynamic system described as a Markov process, we prove a general lower bound for dissipation in terms of the square of the heat current, thus establishing that nonvanishing current inevitably implies dissipation. This leads to a universal trade-off relation between efficiency and power, with which we rigorously prove that a heat engine with nonvanishing power never attains the Carnot efficiency. Our theory applies to systems arbitrarily far from equilibrium, and does not assume any specific symmetry of the model.

Takuma Akimoto, Eli Barkai, Keiji Saito,

Universal Fluctuations of Single-Particle Diffusivity in Quenched Environment,

Physical Review Letters 117, 180602 (2016).

[Summary] Local diffusion coefficients in disordered materials such as living cells are highly heterogeneous. We consider finite systems with quenched disorder in order to investigate the effects of sample disorder fluctuations and confinement on single-particle diffusivity. While the system is ergodic in a single disorder realization, the time-averaged mean square displacement depends crucially on the disorder; i.e., the system is ergodic but non-self-averaging. Moreover, we show that the disorder average of the time-averaged mean square displacement decreases with the system size. We find a universal distribution for diffusivity in the sense that the shape of the distribution does not depend on the dimension. Quantifying the degree of the non-self-averaging effect, we show that fluctuations of single-particle diffusivity far exceed the corresponding annealed theory and also find confinement effects. The relevance for experimental situations is also discussed.

Yoshimichi Teratani, Rui Sakano, Ryo Fujiwara, Tokuro Hata, Tomonori Arakawa, Meydi Ferrier, Kensuke Kobayashi and Akira Oguri,

Field-enhanced Kondo correlations in a half-filling nanotube dot: evolution of an SU(n) Fermi-liquid fixed point,

Journal of the Physical Society of Japan 85, 094718/1-18 (2016).

[Summary] Carbon nanotube quantum dot has four-fold degenerate one-particle levels, which bring a variety to the Kondo effects taking place in a wide tunable-parameter space. We theoretically study an emergent SU(2) symmetry that is suggested by recent magneto-transport measurements, carried out near two electrons filling. It does not couple with the magnetic field, and emerges in the case where the spin and orbital Zeeman splittings cancel each other out in two of the oneparticle levels among four. This situation seems to be realized in the recent experiment. Using the Wilson numerical renormalization group, we show that a crossover from the SU(4) to SU(2) Fermi-liquid behavior occurs as magnetic field increases at two impurity-electrons filling. We also find that the quasiparticles are significantly renormalized as the remaining two one-particle levels move away from the Fermi level and are frozen at high magnetic fields. Furthermore, we consider how the singlet ground state evolves during such a crossover. Specifically, we reexamine the SU(N) Kondo singlet for M impurity-electrons filling in the limit of strong exchange interactions. We find that the nondegenerate Fermi-liquid fixed point of Nozieres and Blandin can be described as abosonic Perron-Frobenius vector for M composite pairs, each of which consists of one impurity-electron and one conduction-hole. This interpretation in terms of the Perron-Frobenius theorem can also be extended to the Fermi-liquid fixed-point without the SU(N) symmetry.

Johannes Stigloher, Martin Decker, Helmut S. Körner, Kenji Tanabe, Takahiro Moriyama, Takuya Taniguchi, Hiroshi Hata, Marco Madami, Gianluca Gubbiotti, Kensuke Kobayashi, Teruo Ono, and Christian H. Back,

Snell’s Law for Spin Waves,

Physical Review Letters 117, 037204/1-4 (2016).

[Summary] We report the experimental observation of Snell’s law for magnetostatic spin waves in thin ferromagnetic Permalloy films by imaging incident, refracted, and reflected waves. We use a thickness step as the interface between two media with different dispersion relations. Since the dispersion relation for magnetostatic waves in thin ferromagnetic films is anisotropic, deviations from the isotropic Snell's law known in optics are observed for incidence angles larger than 25° with respect to the interface normal between the two magnetic media. Furthermore, we can show that the thickness step modifies the wavelength and the amplitude of the incident waves. Our findings open up a new way of spin wave steering for magnonic applications.

Keiji Saito and Abhishek Dhar,

Waiting for rare entropic fluctuations,

Europhys Letters 114, 50004/1-6 (2016).

[Summary] Nonequilibrium fluctuations of various stochastic variables, such as work and entropy production, have been widely discussed recently in the context of large deviations, cumulants and fluctuation relations. Typically one looks at the probability distributions for entropic fluctuations of various sizes to occur in a fixed time interval. An important and natural question is to ask for the time one has to wait to see fluctuations of a desired size. We address this question by studying the first-passage time distribution (FPTD). We derive the general basic equation to get the FPTD for entropic variables. Based on this, the FPTD on entropy production in a driven colloidal particle in the ring geometry is illustrated. A general asymptotic form of the FPTD and integral fluctuation relation symmetry in terms of the first passages are found.

Tatsuya Muro, Yoshitaka Nishihara, Shota Norimoto, Meydi Ferrier, Tomonori Arakawa, *Kensuke Kobayashi, Thomas Ihn, Clemens Rösler, Klaus Ensslin, Christian Reichl, and Werner Wegscheider,

Finite shot noise and electron heating at quantized conductance in high-mobility quantum point contacts,

Physical Review B 93, 195411/1-7 (2016).

[Summary] We report a precise experimental study on the shot noise of a quantum point contact (QPC) fabricated in a GaAs/AlGaAs based high-mobility two-dimensional electron gas (2DEG). The combination of unprecedented cleanliness and very high measurement accuracy has enabled us to discuss the Fano factor to characterize the shot noise with a precision of 0.01. We observed that the shot noise at zero magnetic field exhibits a slight enhancement exceeding the single particle theoretical prediction, and that it gradually decreases as a perpendicular magnetic field is applied. We also confirmed that this additional noise completely vanishes in the quantum Hall regime. These phenomena can be explained by the electron heating effect near the QPC, which is suppressed with increasing magnetic field.

*Aki Kutvonen, Takahiro Sagawa, and Tapio Ala-Nissila,

Thermodynamics of information exchange between two coupled quantum dots,

Phyical Review E 93, 032147/1-7 (2016).

[Summary] We propose a setup based on two coupled quantum dots where thermodynamics of a measurement can be quantitatively characterized. The information obtained in the measurement can be utilized by performing feedback in a manner apparently breaking the second law of thermodynamics. In this way the setup can be operated as a Maxwell's demon, where both the measurement and feedback are performed separately by controlling an external parameter. This is analogous to the case of the original Szilard engine. Since the setup contains both the microscopic demon and the engine itself, the operation of the whole measurement-feedback cycle can be explained in detail at the level of single realizations. In addition, we derive integral fluctuation relations for both the bare and coarse-grained entropy productions in the setup.

Takashi Mori, Tomotaka Kuwahara, Keiji Saito,

Rigorous bound on energy absorption and generic relaxation in periodically driven quantum systems,

Physical Review Letters 116, 120401/1-5 (2016).

[Summary] We discuss the universal nature of relaxation in isolated many-body quantum systems subjected to global and strong periodic driving. Our rigorous Floquet analysis shows that the energy of the system remains almost constant up to an exponentially long time in frequency for arbitrary initial states and that an effective Hamiltonian obtained by a truncation of the Floquet-Magnus expansion is a quasiconserved quantity in a long time scale. These two general properties lead to an intriguing classification on the initial stage of relaxation, one of which is similar to the prethermalization phenomenon in nearly integrable systems.

Shunpei Takeshita, Sadashige Matsuo, Takahiro Tanaka, Shu Nakaharai, Kazuhito Tsukagoshi, Takahiro Moriyama, Teruo Ono, Tomonori Arakawa, and Kensuke Kobayashi,

Anomalous behavior of 1/f noise in graphene near the charge neutrality point,

Applied Physics Letters 108, 103106/1-4 (2016).

[Summary] We investigate the noise in single layer graphene devices from equilibrium to far-from equilibrium and found that the 1/f noise shows an anomalous dependence on the source-drain bias voltage . While the Hooge’s relation is not the case around the charge neutrality point, we found that it is recovered at very low bias region. We propose that the depinning of the electron-hole puddles is induced at finite bias, which may explain this anomalous noise behavior.

Tomotaka Kuwahara, Takashi Mori, and Keiji Saito,

Floquet-Magnus Theory and Generic Transient Dynamics in Periodically Driven Many-Body Quantum Systems,

Annals of Physics, 96-124 (2016).

[Summary] This work explores a fundamental dynamical structure for a wide range of many-body quantum systems under periodic driving. Generically, in the thermodynamic limit, such systems are known to heat up to infinite temperature states after infinite-time evolution, irrespective of dynamical details. In the present study, instead of considering infinitely long-time scale, we aim to provide a framework to understand the long but finite time behavior, namely the transient dynamics. In the analysis, we focus on the Floquet-Magnus (FM) expansion that gives a formal expression of the effective Hamiltonian on the system. Although in general the full series expansion is not convergent in the thermodynamics limit, we give a clear relationship between the FM expansion and the transient dynamics. More precisely, we rigorously show that a truncated version of the FM expansion accurately describes the exact dynamics for a finite-time scale.

*Kenji Tanabe, Ryo Matsumoto, Jun-Ichiro Ohe, Shuichi Murakami, Takahiro Moriyama, Daichi Chiba, Kensuke Kobayashi and Teruo Ono,

Observation of magnon Hall-like effect for sample-edge scattering in unsaturated YIG,

physica status solidi (b) 253, 783-787 (2016).

[Summary] We report the observation of a magnon Hall-like effect for the scattering of magnons at the sample edge in Y3Fe5O12 crystals. The experiments are performed under an out-of-plane magnetic field at room temperature using an infrared thermometry. When the magnons are incident into the sample edge in the unsaturated magnetic structure, appreciable transverse thermal gradient is detected. This thermal gradient could be attributed to magnon Hall effect for sample-edge scattering. We unexpectedly find that this effect is largely enhanced in the unsaturated regime, compared with the saturated regime where theoretical mechanism of magnon Hall effect due to the Berry curvature has been proposed previously.

Naoto Shiraishi, Takumi Matsumoto, and Takahiro Sagawa,

Measurement-feedback formalism meets information reservoirs,

New Journal of Physics 18, 013044/1-8 (2016).

[Summary] There have been two distinct formalisms of thermodynamics of information: one is the measurement-feedback formalism, which concerns bipartite systems with measurement and feedback processes, and the other is the information reservoir formalism, which considers bit sequences as a thermodynamic fuel. In this paper, we derive a second-law-like inequality by applying the measurement-feedback formalism to information reservoirs, which provides a stronger bound of extractable work than any other known inequality in the same setup. In addition, we demonstrate that the Mandal-Jarzynski model, which is a prominent model of the information reservoir formalism, is equivalent to a model obtained by the contraction of a bipartite system with autonomous measurement and feedback. Our results provide a unified view on the measurement-feedback and the information-reservoir formalisms.

*Tokuro Hata, Tomonori Arakawa, Kensaku Chida, Sadashige Matsuo, and Kensuke Kobayashi,

Giant Fano factor and bistability in a Corbino disk in the quantum Hall effect breakdown regime,

Journal of Physics: Condensed Matter 28, 055801/1-7 (2016).

[Summary] We performed noise measurements for a Corbino disk in the quantum Hall effect breakdown regime. We investigated two Corbino-disk-type devices with different sizes and observed that the Fano factor increases when the length between the contacts doubles. This observation is consistent with the avalanche picture suggested by the bootstrap electron heating model. The temperature dependence of the Fano factor indicates that the avalanche effect becomes more prominent as temperature decreases. Moreover, in the highly nonlinear regime, negative differential resistance and temporal oscillation due to bistability are found. A possible interpretation of this result is that Zener tunneling of electrons between Landau levels occurs.

*Meydi Ferrier, Tomonori Arakawa, Tokuro Hata, Ryo Fujiwara, Raphaëlle Delagrange, Raphael Weil, Richard Deblock, Rui Sakano, Akira Oguri, and *Kensuke Kobayashi,

Universality of non-equilibrium fluctuations in strongly correlated quantum liquids,

Nature Physics 12, 230-235 (2015).

[Summary] Interacting quantum many-body systems constitute a fascinating research field because they form quantum liquids with remarkable properties and universal behavior. In fermionic systems, such quantum liquids are realized in helium-3 liquid, heavy fermion systems, neutron stars and cold gases. Their properties in the linear-response regime have been successfully described by the theory of Fermi liquids. The idea is that they behave as an ensemble of non-interacting‘quasi-particles’. However, non-equilibrium properties have still to be established and remain a key issue of many-body physics. Here, we show a precise experimental demonstration of Landau Fermi liquid theory extended to the non-equilibrium regime in a zero-dimensional system. Combining transport and ultra-sensitive current noise measurements, we have unambiguously identified the SU(2) and SU(4) symmetries of a quantum liquid in a carbon nanotube tuned in the universal Kondo regime. Whereas the free quasi-particle picture is found valid around equilibrium, an enhancement of the current fluctuations is detected out of equilibrium and perfectly explained by an effective charge induced by the residual interaction between quasi-particles. Moreover, an as-yet-unknown scaling law for the effective charge is discovered, suggesting a new non-equilibrium universality.

#### 2015

*Sadashige Matsuo, Shunpei Takeshita, Takahiro Tanaka, Shu Nakaharai, Kazuhito Tsukagoshi, Takahiro Moriyama, Teruo Ono, Kensuke Kobayashi,

Edge mixing dynamics in graphene p–n junctions in the quantum Hall regime,

Nature Communications 6, 8066/1-6 (2015).

[Summary] Massless Dirac electron systems such as graphene exhibit a distinct half-integer quantum Hall effect, and in the bipolar transport regime co-propagating edge states along the pn junction are realized. Additionally, these edge states are uniformly mixed at the junction, which makes it a unique structure to partition electrons in these edge states. Although many experimental works have addressed this issue, the microscopic dynamics of electron partition in this peculiar structure remains unclear. Here we performed shot-noise measurements on the junction in the quantum Hall regime as well as at zero magnetic field. We found that, in sharp contrast with the zero-field case, the shot noise in the quantum Hall regime is finite in the bipolar regime, but is strongly suppressed in the unipolar regime. Our observation is consistent with the theoretical prediction and gives microscopic evidence that the edge states are uniquely mixed along the pn junction.

Kay Brandner, Keiji Saito, and Udo Seifert ,

Thermodynamics of Micro- and Nano-Systems Driven by Periodic Temperature Variations,

Physical Review X 5, 031019 (2015).

[Summary] We introduce a general framework for analyzing the thermodynamics of small systems that are driven by both a periodic temperature variation and some external parameter modulating their energy. We show how to express total entropy production by properly identified time-independent affinities and currents without making a linear response assumption. In linear response, kinetic coefficients akin to Onsager coefficients can be identified. Specializing to a Fokker-Planck-type dynamics, we show that these coefficients can be expressed as a sum of an adiabatic contribution and one reminiscent of a Green-Kubo expression that contains deviations from adiabaticity. Furthermore, we show that the generalized kinetic coefficients fulfill an Onsager-Casimir-type symmetry tracing back to microscopic reversibility. This symmetry allows for nonidentical off-diagonal coefficients if the driving protocols are not symmetric under time reversal. We then derive a novel constraint on the kinetic coefficients that is sharper than the second law and provides an efficiency-dependent bound on power.

*Sadashige Matsuo, Shu Nakaharai, Katsuyoshi Komatsu, Kazuhito Tsukagoshi, Takahiro Moriyama, Teruo Ono, and Kensuke Kobayashi,

Parity effect of bipolar quantum Hall edge transport around graphene antidots,

Scientific Reports 5, 11723/1-7 (2015).

[Summary] Parity effect, which means that even-odd property of an integer physical parameter results in an essential difference, ubiquitously appears and enables us to grasp its physical essence as the microscopic mechanism is less significant in coarse graining. Here we report a new parity effect of quantum Hall edge transport in graphene antidot devices with pn junctions (PNJs). We found and experimentally verified that the bipolar quantum Hall edge transport is drastically affected by the parity of the number of PNJs. This parity effect is universal in bipolar quantum Hall edge transport of not only graphene but also massless Dirac electron systems. These results offer a promising way to design electron interferometers in graphene.

*Sosuke Ito, Takahiro Sagawa,

Maxwell’s demon in biochemical signal transduction with feedback loop,

Nature Communications 6, 7498 (2015).

[Summary] Signal transduction in living cells is vital to maintain life itself, where information transfer in noisy environment plays a significant role. In a rather different context, the recent intensive researches of "Maxwell's demon" - a feedback controller that utilizes information of individual molecules - has led to a unified theory of information and thermodynamics. Here we combine these two streams of researches, and show that the second law of thermodynamics with information reveals the fundamental limit of the robustness of signal transduction against environmental fluctuations. Especially, we found that the degree of robustness is quantitatively characterized by an informational quantity called transfer entropy. Our information-thermodynamic approach is applicable to biological communication inside cells, in which there is no explicit channel coding in contrast to artificial communication. Our result would open up a novel biophysical approach to understand information processing in living systems on the basis of the fundamental information-thermodynamics link.

Kiyoshi Kanazawa, Tomohiko G. Sano, Takahiro Sagawa, and Hisao Hayakawa,

Asymptotic Derivation of Langevin-like Equation with Non-Gaussian Noise and Its Analytical Solution,

Journal of Statistical Physics 160, 1294-1335 (2015).

*Naoto Shiraishi, Sosuke Ito, Kyogo Kawaguchi, and Takahiro Sagawa,

Role of measurement-feedback separation in autonomous Maxwell’s demons,

New Journal of Physics 17, 045012/1-11 (2015).

[Summary] We introduce an information heat engine that is autonomous (i.e., without any time-dependent parameter) but has separated measurement and feedback processes. This model serves as a bridge between different types of information heat engines inspired by Maxwell's demon; from the original Szilard-engine type systems to the autonomous demonic setups. By analyzing our model on the basis of a general framework introduced in our previous paper (Shiraishi and Sagawa 2015 Phys. Rev. E 91 012130), we clarify the role of the separation of measurement and feedback in the integral fluctuation theorems.

*Kiyoshi Kanazawa, Tomohiko G. Sano, Takahiro Sagawa, and Hisao Hayakawa,

Minimal Model of Stochastic Athermal Systems: Origin of Non-Gaussian Noise,

Physical Review Letters 114, 090601/1-10 (2015).

[Summary] For a wide class of stochastic athermal systems, we derive Langevin-like equations driven by non-Gaussian noise, starting from master equations and developing a new asymptotic expansion. We found an explicit condition whereby the non-Gaussian properties of the athermal noise become dominant for tracer particles associated with both thermal and athermal environments. Furthermore, we derive an inverse formula to infer microscopic properties of the athermal bath from the statistics of the tracer particle. We apply our formulation to a granular motor under viscous friction and analytically obtain the angular velocity distribution function. Our theory demonstrates that the non-Gaussian Langevin equation is the minimal model of athermal systems.

*Juan M. R. Parrondo, Jordan M. Horowitz, and Takahiro Sagawa,

Thermodynamics of information,

Nature Physics 11, 131-139 (2015).

[Summary] By its very nature, the second law of thermodynamics is probabilistic, in that its formulation requires a probabilistic description of the state of a system. This raises questions about the objectivity of the second law: does it depend, for example, on what we know about the system? For over a century, much effort has been devoted to incorporating information into thermodynamics and assessing the entropic and energetic costs of manipulating information. More recently, this historically theoretical pursuit has become relevant in practical situations where information is manipulated at small scales, such as in molecular and cell biology, artificial nano-devices or quantum computation. Here we give an introduction to a novel theoretical framework for the thermodynamics of information based on stochastic thermodynamics and fluctuation theorems, review some recent experimental results, and present an overview of the state of the art in the field.

*Naoto Shiraishi and Takahiro Sagawa,

Fluctuation theorem for partially masked nonequilibrium dynamics,

Physical Review E 91, 012130/1-7 (2015).

[Summary] We establish a generalization of the fluctuation theorem for partially masked nonequilibrium dynamics. We introduce a partial entropy production with a subset of all possible transitions, and show that the partial entropy production satisfies the integral fluctuation theorem. Our result reveals the fundamental properties of a broad class of autonomous as well as nonautonomous nanomachines. In particular, our result gives a unified fluctuation theorem for both autonomous and nonautonomous Maxwell's demons, where mutual information plays a crucial role. Furthermore, we derive a fluctuation-dissipation theorem that relates nonequilibrium stationary current to two kinds of equilibrium fluctuations.

*Tomonori Arakawa, Junichi Shiogai, Mariusz Ciorga, Martin Utz, Dieter Schuh, Makoto Kohda, Junsaku Nitta, Dominique Bougeard, Dieter Weiss, Teruo Ono, and Kensuke Kobayashi,

Shot noise induced by nonequilibrium spin accumulation,

Physical Review Letters 114, 016601/1-5 (2015).

[Summary] When an electric current passes across a potential barrier, the partition process of electrons at the barrier gives rise to the shot noise, reflecting the discrete nature of the electric charge. Here we report the observation of excess shot noise connected with a spin current which is induced by a nonequilibrium spin accumulation in an all-semiconductor lateral spin-valve device. We find that this excess shot noise is proportional to the spin current. Additionally, we determine quantitatively the spin-injection-induced electron temperature by measuring the current noise. Our experiments show that spin accumulation driven shot noise provides a novel means of investigating nonequilibrium spin transport.

#### 2014

*Takahiro Tanaka, Tomonori Arakawa, Masahiro Maeda, Kensuke Kobayashi, Yoshitaka Nishihara, Teruo Ono, Takayuki Nozaki, Akio Fukushima, and Shinji Yuasa,

Leak current estimated from the shot noise in magnetic tunneling junctions,

Applied Physics Letters 105, 042405/1-4 (2014).

[Summary] We performed the shot noise measurement in epitaxial Fe/MgO/Fe-based magnetic tunneling junctions (MTJs) with various MgO thicknesses between 1.1 nm and 1.625nm. While the Fano factor to characterize the shot noise is very close to 1 in MTJs with MgO barrier thicker than 1.2nm, the magnetic configuration-dependent reduction of the Fano factor for MTJs with thin MgO barrier was observed, which is mainly due to the existence of leakage current. By using a simple parallel circuit model, we demonstrated that the contribution of the leak current can be sensitively derived from the shot noise.

Suman G. Das, Abhishek Dhar, Keiji Saito, Christian B. Mendl, Herbert Spohn,

Numerical test of hydrodynamic fluctuation theory in the Fermi-Pasta-Ulam chain,

Physical Review E 90, 12124/1-11 (2014).

[Summary] Recent work has developed a nonlinear hydrodynamic fluctuation theory for a chain of coupled anharmonic oscillators governing the conserved fields, namely stretch, momentum, and energy. The linear theory yields two propagating sound modes and one diffusing heat mode. In contrast, the nonlinear theory predicts that, at long times, the sound mode correlations satisfy Kardar-Parisi-Zhang (KPZ) scaling, while the heat mode correlations satisfies Levy-walk scaling. In the present contribution we report on molecular dynamics simulations of Fermi-Pasta-Ulam chains to compute various spatiotemporal correlation functions and compare them with the predictions of the theory. We find very good agreement in many cases, but also some deviations.

*Kiyoshi Kanazawa, Takahiro Sagawa, and Hisao Hayakawa,

Energy pumping in electrical circuits under avalanche noise,

Physical Review E 90, 012115/1-8 (2014).

[Summary] We theoretically study energy pumping processes in an electrical circuit with avalanche diodes, where non-Gaussian athermal noise plays a crucial role. We show that a positive amount of energy (work) can be extracted by an external manipulation of the circuit in a cyclic way, even when the system is spatially symmetric. We discuss the properties of the energy pumping process for both quasistatic and finite-time cases, and analytically obtain formulas for the amounts of the work and the power. Our results demonstrate the significance of the non-Gaussianity in energetics of electrical circuits.

*Jordan M. Horowitz and Takahiro Sagawa,

Equivalent Definitions of the Quantum Nonadiabatic Entropy Production,

Journal of Statistical Physics 156, 55-65 (2014).

[Summary] The nonadiabatic entropy production is a useful tool for the thermodynamic analysis of continuously dissipating, nonequilibrium steady states. For open quantum systems, two seemingly distinct definitions for the nonadiabatic entropy production have appeared in the literature, one based on the quantum relative entropy and the other based on quantum trajectories. We show that these two formulations are equivalent. Furthermore, this equivalence leads us to a proof of the monotonicity of the quantum relative entropy under a special class of completely-positive, trace-preserving quantum maps, which circumvents difficulties associated with the noncommuntative structure of operators.

*Kensaku Chida, Tokuro Hata, Tomonori Arakawa, Sadashige Matsuo, Yoshitaka Nishihara, Takahiro Tanaka, Teruo Ono, and Kensuke Kobayashi,

Avalanche electron bunching in a Corbino disk in the quantum Hall effect breakdown regime,

Physical Review B 89, 235318/1-4 (2014).

[Summary] We have measured the current noise in a device with Corbino geometry to investigate the dynamics of electrons in the breakdown regime of the integer quantum Hall effect (QHE). In the breakdown regime, the Fano factor of the current noise exceeds 103, which indicates the presence of electron bunching. As super-Poissonian current noise is observed only in the breakdown regime, the bunching effect is related to the QHE breakdown. These observations support a QHE breakdown mechanism that involves an electron avalanche.

*Jonne V. Koski, Ville F. Maisi, Takahiro Sagawa, and Jukka P. Pekola,

Experimental Observation of the Role of Mutual Information in the Nonequilibrium Dynamics of a Maxwell Demon,

Physical Review Letters 113, 030601/1-5 (2014).

[Summary] We validate experimentally a fluctuation relation known as generalized Jarzynski equality governing the work distribution in a feedback-controlled system. The feedback control is performed on a single electron box analogously to the original Szilard engine. In the generalized Jarzynski equality, mutual information is treated on an equal footing with the thermodynamic work. Our measurements provide the first evidence of the role of mutual information in the fluctuation theorem and thermodynamics of irreversible processes.

*Kyogo Kawaguchi, Shin-ichi Sasa, and Takahiro Sagawa,

Nonequilibrium Dissipation-free Transport in F1-ATPase and the Thermodynamic Role of Asymmetric Allosterism,

Biophysical Journal 106, 2450–2457 (2014).

[Summary] F1-ATPase (or F1), the highly efficient and reversible biochemical engine, has motivated physicists as well as biologists to imagine the design principles governing machines in the fluctuating world. Recent experiments have clarified yet another interesting property of F1; the dissipative heat inside the motor is very small, irrespective of the velocity of rotation and energy transport. Conceptual interest is devoted to the fact that the amount of internal dissipation is not simply determined by the sequence of equilibrium pictures, but also relies on the rotational-angular dependence of nucleotide affinity, which is a truly nonequilibrium aspect. We propose that the totally asymmetric allosteric model (TASAM), where adenosine triphosphate (ATP) binding to F1 is assumed to have low dependence on the angle of the rotating shaft, produces results that are most consistent with the experiments. Theoretical analysis proves the crucial role of two time scales in the model, which explains the universal mechanism to produce the internal dissipation-free feature. The model reproduces the characteristic torque dependence of the rotational velocity of F1 and predicts that the internal dissipation upon the ATP synthesis direction rotation becomes large at the low nucleotide condition.

*Kenji Tanabe, Ryo Matsumoto, Jun-ichiro Ohe, Shuichi Murakami, Takahiro Moriyama, Daichi Chiba, Kensuke Kobayashi, and Teruo Ono,

Real-time observation of Snell’s law for spin waves in a thin ferromagnetic film,

Applied Physics Express 7, 053001/1-4 (2014).

[Summary] We report the real-time observation of spin-wave propagation across a step inserted between two ferromagnetic films with different thicknesses. Because the dispersion relation of the spin wave depends on the thickness of the film, the step works as a junction to affect the spin wave propagation. When the spin wave transmits through the junction, the wavenumber undergoes modulation as per Snell’s law, which states that the refraction index is proportional to the wavenumber. From the viewpoint of magnonics, the present achievement opens up new possibilities of controlling the wavenumber of spin waves.

Julian Stark, Kay Brandner, Keiji Saito, and Udo Seifert,

A Classical Nernst Engine,

Physical Review Letters 112, 140601/1-5 (2014).

[Summary] We introduce a simple model for an engine based on the Nernst effect. In the presence of a magnetic field, a vertical heat current can drive a horizontal particle current against a chemical potential. For a microscopic model invoking classical particle trajectories subject to the Lorentz force, we prove a universal bound 0.172 for the ratio between the maximum efficiency and the Carnot efficiency. This bound, as the slightly lower one 1/6 for efficiency at maximum power, can indeed be saturated for a large magnetic field and small fugacity.

*Takahiro Sagawa,

Thermodynamic and Logical Reversibilities Revisited,

Journal of Statistical Mechanics, 1-33 (2014).

[Summary] We review and investigate the general theory of the thermodynamics of computation, and derive the fundamental inequalities that set the lower bounds of the work requirement and the heat emission during a computation. These inequalities constitute the generalized Landauer principle, where the information contents are involved in the second law of thermodynamics. We discuss in detail the relationship between the thermodynamic and logical reversibilities; the former is related to the entropy production in the total system including a heat bath, while the latter is related to the entropy change only in the logical states of the memory. In particular, we clarify that any logically irreversible computation can be performed in a thermodynamically reversible manner in the quasi-static limit, which does not contradict the conventional Landauer principle. Our arguments would serve as the theoretical foundation of the thermodynamics of computation in terms of modern statistical physics.

#### 2013

*Takahiro Sagawa and Masahito Ueda,

Role of mutual information in entropy production under information exchanges,

New Journal of Physics 15, 125012/1-23 (2013).

[Summary] We relate the information exchange between two stochastic systems to the nonequilibrium entropy production in the whole system. By deriving a general formula that decomposes the total entropy production into the thermodynamic and informational parts, we obtain nonequilibrium equalities such as the fluctuation theorem in the presence of information processing. Our results apply not only to situations under measurement and feedback control but also to those under multiple information exchanges between two systems, giving the fundamental energy cost for information processing and elucidating the thermodynamic and informational roles of a memory in information processing. We point out a dual relationship between measurement and feedback.

*Jung Jun Park, Kang-Hwan Kim, Takahiro Sagawa, and Sang Wook Kim,

Heat Engine Driven by Purely Quantum Information,

Physical Review Letters 111, 230402/1-5 (2013).

[Summary] The key question of this Letter is whether work can be extracted from a heat engine by using purely quantum mechanical information. If the answer is yes, what is its mathematical formula? First, by using a bipartite memory we show that the work extractable from a heat engine is bounded not only by the free energy change and the sum of the entropy change of an individual memory but also by the change of quantum mutual information contained inside the memory. We then find that the engine can be driven by purely quantum information, expressed as the so-called quantum discord, forming a part of the quantum mutual information. To confirm it, as a physical example we present the Szilard engine containing a diatomic molecule with a semipermeable wall.

*Keiji Saito and Takeo Kato,

Kondo signature in heat transfer via a local two-state system,

Physical Review Letters 111, 214301/1-4 (2013).

[Summary] We study the Kondo effect in heat transport via a local two-state system. This system is described by the spin-boson Hamiltonian with Ohmic dissipation, which can be mapped onto the Kondo model with anisotropic exchange coupling. We calculate thermal conductance by the Monte Carlo method based on the exact formula. Thermal conductance has a scaling formκ=(k2BTK/ℏ)f(α,T/TK) , whereTK andα indicate the Kondo temperature and dimensionless coupling strength, respectively. Temperature dependence of conductance is classified by the Kondo temperature asκ∝(T/TK)3 forT≪TK andκ∝(kBT/ℏωc)2α−1 forT≫TK . Similarities to the Kondo signature in electric transport are discussed.

*Tatsuro Yuge, Takahiro Sagawa, Ayumu Sugita, and Hisao Hayakawa,

Geometrical Excess Entropy Production in Nonequilibrium Quantum Systems,

Journal of Statistical Physics 153, 412-441 (2013).

[Summary] For open systems described by the quantum Markovian master equation, we study a possible extension of the Clausius equality to quasistatic operations between nonequilibrium steady states (NESSs). We investigate the excess heat divided by temperature (i.e., excess entropy production) which is transferred into the system during the operations. We derive a geometrical expression for the excess entropy production, which is analogous to the Berry phase in unitary evolution. Our result implies that in general one cannot define a scalar potential whose difference coincides with the excess entropy production in a thermodynamic process, and that a vector potential plays a crucial role in the thermodynamics for NESSs. In the weakly nonequilibrium regime, we show that the geometrical expression reduces to the extended Clausius equality derived by Saito and Tasaki (J. Stat. Phys. 145:1275, 2011). As an example, we investigate a spinless electron system in quantum dots. We find that one can define a scalar potential when the parameters of only one of the reservoirs are modified in a non-interacting system, but this is no longer the case for an interacting system.

Sosuke Ito and Takahiro Sagawa,

Information Thermodynamics on Causal Networks,

Physical Review Letters 111, 180603/1-6 (2013).

[Summary] We study nonequilibrium thermodynamics of complex information flows induced by interactions between multiple fluctuating systems. Characterizing nonequilibrium dynamics by causal networks (i.e., Bayesian networks), we obtain novel generalizations of the second law of thermodynamics and the fluctuation theorem, which include an informational quantity characterized by the topology of the causal network. Our result implies that the entropy production in a single system in the presence of multiple other systems is bounded by the information flow between these systems. We demonstrate our general result by a simple model of biochemical adaptation.

*Sang Wook Kim, Kang-Hwan Kim, Takahiro Sagawa, Simone De Liberato, and Masahito Ueda,

Kim et al. Reply:,

Physical Review Letters 111, 188902/1 (2013).

[Summary] A Reply to the Comment by M. Plesch et al.

*Sadashige Matsuo, Kensaku Chida, Daichi Chiba, Teruo Ono, Keith Slevin, Kensuke Kobayashi, Tomi Ohtsuki, Cui-Zu Chang, Ke He, Xu-Cun Ma, and Qi-Kun Xue,

Experimental Proof of Universal Conductance Fluctuation in Quasi-1D Epitaxial Bi_{2}Se_{3} Wires,

Physical Review B 88, 155438/1-8 (2013).

[Summary] We report on conductance fluctuation in quasi-one-dimensional wires made of epitaxial Bi2Se3 thin film. We found that this type of fluctuation decreases as the wire length becomes longer and that the amplitude of the fluctuation is well scaled to the coherence, thermal diffusion, and wire lengths, as predicted by conventional universal conductance fluctuation (UCF) theory. Additionally, the amplitude of the fluctuation can be understood to be equivalent to the UCF amplitude of a system with strong spin-orbit interaction and no time-reversal symmetry. These results indicate that the conductance fluctuation in Bi2Se3 wires is explainable through UCF theory. This work verifies the scaling relationship of UCF in a system with strong spin-orbit interaction.

*Tomonori Arakawa, Yoshitaka Nishihara, Masahiro Maeda, Shota Norimoto, and Kensuke Kobayashi,

Cryogenic amplifier for shot noise measurement at 20 mK,

Applied Physics Letters 103, 172104/1-4 (2013).

[Summary] We developed a shot noise measurement system for mesoscopic conductors (typical resistance h/2e^2) at very low temperature (20 mK). To realize required high-resolution measurement, we made a high-electron-mobility-transistor (HEMT)-based cryogenic amplifier working at a target frequency range (@2.5 MHz), whose gain flatness and input voltage noise were carefully tuned. We can suppress the 1/f noise of the amplifier by using two HEMTs in parallel. The performance of the noise measurement system at 20mK was demonstrated for a quantum point contact with high experimental accuracy below 10^-29 A^2/Hz.

*Jonne V. Koski, Takahiro Sagawa, O-P. Saira, Y. Yoon, A. Kutvonen, P. Solinas, M. Möttönen, T. Ala-Nissila, and Jukka P. Pekola,

Distribution of entropy production in a single-electron box,

Nature Physics 9, 644-648 (2013).

[Summary] Recently, the fundamental laws of thermodynamics have been reconsidered for small systems. The discovery of the fluctuation relations has spurred theoretical and experimental studies. The concept of entropy production has been extended to the microscopic level by considering stochastic trajectories of a system coupled to a heat bath. However, this has not been studied experimentally if there are multiple thermal baths present. Here, we measure, with high precision, the distributions of microscopic entropy production in a single-electron box consisting of two islands with a tunnel junction. The islands are coupled to separate heat baths at different temperatures, maintaining a steady thermal non-equilibrium. We demonstrate that stochastic entropy production from trajectories of electronic transitions is related to thermodynamic entropy production from dissipated heat in the respective thermal baths. We verify experimentally that the fluctuation relations for both definitions are satisfied. Our results reveal the subtlety of irreversible entropy production in non-equilibrium.

*Jordan M. Horowitz, Takahiro Sagawa, and Juan M. R. Parrondo,

Imitating Chemical Motors with Optimal Information Motors,

Physical Review Letters 111, 010602/1-5 (2013).

[Summary] To induce transport, detailed balance must be broken. A common mechanism is to bias the dynamics with a thermodynamic fuel, such as chemical energy. An intriguing, alternative strategy is for a Maxwell demon to effect the bias using feedback. We demonstrate that these two different mechanisms lead to distinct thermodynamics by contrasting a chemical motor and information motor with identical dynamics. To clarify this difference, we study both models within one unified framework, highlighting the role of the interaction between the demon and the motor. This analysis elucidates the manner in which information is incorporated into a physical system.

*Kiyoshi Kanazawa, Takahiro Sagawa, and Hisao Hayakawa,

Heat conduction induced by non-Gaussian athermal fluctuations,

Physical Review E 87, 052124/1-10 (2013).

[Summary] We study the properties of heat conduction induced by non-Gaussian noises from athermal environments. We find that new terms should be added to the conventional Fourier law and the fluctuation theorem for the heat current, where its average and fluctuation are determined not only by the noise intensities but also by the non-Gaussian nature of the noises. Our results explicitly show the absence of the zeroth law of thermodynamics in athermal systems.