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A01-001 SASA

Paper | Original Paper

2017

*Masahiko Ueda, Shin-ichi Sasa,
Replica symmetry breaking in trajectory space for the trap model,
Journal of Physics A: Mathematical and Theoretical 50, 125001/1-14 (2017).

[Summary] We study the localization in the one-dimensional trap model in terms of statistical mechanics of trajectories. By numerically investigating overlap between trajectories of two particles on a common disordered potential, we find that there is a phase transition in the path ensemble. We characterize the low temperature phase as a replica symmetry breaking phase in trajectory space.

*Masato Itami, Shin-ichi Sasa,
Universal Form of Stochastic Evolution for Slow Variables in Equilibrium Systems,
Journal of Statistical Physics 167, 46-63 (2017).

[Summary] Nonlinear, multiplicative Langevin equations for a complete set of slow variables in equilibrium systems are generally derived on the basis of the separation of time scales. The form of the equations is universal and equivalent to that obtained by Green. An equation with a nonlinear friction term for Brownian motion turns out to be an example of the general results. A key method in our derivation is to use different discretization schemes in a path integral formulation and the corresponding Langevin equation, which also leads to a consistent understanding of apparently different expressions for the path integral in previous studies.

2016

Yoshiyuki Chiba and *Naoko Nakagawa,
Numerical determination of entropy associated with excess heat in steady-state thermodynamics,
Physical Review E 94, 022115/1-10 (2016).

[Summary] We numerically determine the global entropy for heat-conducting states, which is connected to the so-called excess heat considered as a basic quantity for steady-state thermodynamics in nonequilibrium. We adopt an efficient method to estimate the global entropy from the bare heat current and find that the obtained entropy agrees with the familiar local equilibrium hypothesis well. Our method possesses a wider applicability than local equilibrium and opens a possibility to compare thermodynamic properties of complex systems in nonequilibrium with those in the local equilibrium. We further investigate the global entropy for heat-conducting states and find that it exhibits both extensive and additive properties; however, the two properties do not degenerate each other differently from those at equilibrium. The separation of the extensivity and additivity makes it difficult to apply powerful thermodynamic methods to the nonequilibrium steady states.

Shou-Wen Wang, Kyogo Kawaguchi, Shin-ichi Sasa, and Lei-Han Tang,
Entropy Production of Nanosystems with Time Scale Separation,
Physical Review Letters 117, 070601/1-070601-5 (2016).

[Summary] Energy flows in biomolecular motors and machines are vital to their function. Yet experimental observations are often limited to a small subset of variables that participate in energy transport and dissipation. Here we show, through a solvable Langevin model, that the seemingly hidden entropy production is measurable through the violation spectrum of the fluctuation-response relation of a slow observable. For general Markov systems with time scale separation, we prove that the violation spectrum exhibits a characteristic plateau in the intermediate frequency region. Despite its vanishing height, the plateau can account for energy dissipation over a broad time scale. Our findings suggest a general possibility to probe hidden entropy production in nanosystems without direct observation of fast variables.

Shin-ichi Sasa, Yuki Yokokura,
Thermodynamic entropy as a Noether invariant,
Physical Review Letters 116, 140601/1-140601/6 (2016).

[Summary] We study a classical many-particle system with an external control represented by a time-dependent extensive parameter in a Lagrangian. We show that thermodynamic entropy of the system is uniquely characterized as the Noether invariant associated with a symmetry for an infinitesimal nonuniform time translation t→t+ηℏβ, where η is a small parameter, ℏ is the Planck constant, β is the inverse temperature that depends on the energy and control parameter, and trajectories in the phase space are restricted to those consistent with quasistatic processes in thermodynamics.

Christian Van den Broeck, Shin-ichi Sasa, Udo Seifert,
Focus on stochastic thermodynamics,
New Journal of Physics 18, 020401-020403 (2016).

[Summary] We introduce the thirty papers collected in this 'focus on' issue. The contributions explore conceptual issues within and around stochastic thermodynamics, use this framework for the theoretical modeling and experimental investigation of specific systems, and provide further perspectives on and for this active field.

2015

Masato Itami and Shin-ichi Sasa,
Derivation of Stokes’ Law from Kirkwood’s Formula and the Green-Kubo Formula via Large Deviation Theory,
Journal of Statistical Physics 161, 532-552 (2015).

[Summary] We study the friction coefficient of a macroscopic sphere in a viscous fluid at low Reynolds number. First, Kirkwood’s formula for the friction coefficient is reviewed on the basis of the Hamiltonian description of particle systems. According to this formula, the friction coefficient is expressed in terms of the stress correlation on the surface of the macroscopic sphere. Then, with the aid of large deviation theory, we relate the surface stress correlation to the stress correlation in the bulk of the fluid, where the latter is characterized by the viscosity in the Green–Kubo formula. By combining Kirkwood’s formula and the Green–Kubo formula in large deviation theory, we derive Stokes’ law without explicitly employing the hydrodynamic equations.

Masahiko Ueda and Shin-ichi Sasa,
Replica symmetry breaking in trajectories of a driven Brownian particle,
Physical Review Letters 115, 080605/1-5 (2015).

[Summary] We study a Brownian particle passively driven by a field obeying the noisy Burgers’ equation. We demonstrate that the system exhibits replica symmetry breaking in the path ensemble with the initial position of the particle being fixed. The key step of the proof is that the path ensemble with a modified boundary condition can be exactly mapped onto the canonical ensemble of directed polymers.

Teruhisa S. Komatsu, Naoko Nakagawa, Shin-ichi Sasa, and Hal Tasaki,
Exact equalities and thermodynamic relations for nonequilibrium steady states,
Journal of Statistical Physics 159, 1237-1285 (2015).

[Summary] We study thermodynamic operations which bring a nonequilibrium steady state (NESS) to another NESS in physical systems under nonequilibrium conditions. We model the system by a suitable Markov jump process, and treat thermodynamic operations as protocols according to which the external agent varies parameters of the Markov process. Then we prove, among other relations, a NESS version of the Jarzynski equality and the extended Clausius relation. The latter can be a starting point of thermodynamics for NESS. We also find that the corresponding nonequilibrium entropy has a microscopic representation in terms of symmetrized Shannon entropy in systems where the microscopic description of states involves "momenta". All the results in the present paper are mathematically rigorous.

*Taiki Haga,
Nonequilibrium Langevin equation and effective temperature for particle interacting with spatially extended environment,
Journal of Statistical Physics 159, 713-729 (2015).

[Summary] We investigate a novel type of Langevin model that describes the nonequilibrium dynamics of a classical particle interacting with a spatially extended environment. In this model, a particle, which interacts with the environment through the nonlinear interaction Hamiltonian, is driven by a constant external force, and subsequently, it reaches a nontrivial nonequilibrium steady state. We derive an effective Langevin equation for the particle in the nonequilibrium steady states. Using this equation, we calculate the effective temperature defined as the ratio of the correlation function of the velocity fluctuation to the linear response function with respect to a small perturbation. As a result, it is shown that the effective temperature associated with the time scale of the particle is identical to the kinetic temperature if the time scale of the environment and that of the particle are well separated. Furthermore, a noteworthy expression, which relates the kinetic temperature with the curvature of the driving force-mean velocity curve, is derived.

*Shin-ichi Sasa,
Collective dynamics from stochastic thermodynamics,
New Journal of Physics 17, 045024/1-14 (2015).

[Summary] From a viewpoint of stochastic thermodynamics, we derive equations that describe the collective dynamics near the order-disorder transition in the globally coupled XY model and near the synchronization-desynchronization transition in the Kuramoto model. A new way of thinking is to interpret the deterministic time evolution of a macroscopic variable as an external operation to a thermodynamic system. We then find that the irreversible work determines the equation for the collective dynamics. When analyzing the Kuramoto model, we employ a generalized concept of irreversible work which originates from a non-equilibrium identity associated with steady state thermodynamics. (IOP SELECT)

Masato Itami and Shin-ichi Sasa,
Nonequilibrium Statistical Mechanics for Adiabatic Piston Problem,
Journal of Statistical Physics 158, 37-56 (2015).

[Summary] We consider the dynamics of a freely movable wall of mass M with one degree of freedom that separates a long tube into two regions, each of which is filled with rarefied gas particles of mass m. The gases are initially prepared at equal pressure but different temperatures, and we assume that the pressure and temperature of gas particles before colliding with the wall are kept constant over time in each region. We elucidate the energetics of the setup on the basis of the local detailed balance condition, and then derive the expression for the heat transferred from each gas to the wall. Furthermore, by using the condition, we obtain the linear response formula for the steady velocity of the wall and steady energy flux through the wall. Using perturbation expansion in a small parameter ϵ≡m/M−−−−−√, we calculate the steady velocity up to order ϵ.

2014

Takahiro Nemoto, Vivien Lecomte, Shin-ichi Sasa, and *Friédéric van Wijland,
Finite size effects in a mean-field kinetically constrained model: dynamical glassiness and quantum criticality,
Journal of Statistical Mechanics -, P10001/1-38 (2014).

[Summary] On the example of a mean-field Fredrickson-Andersen kinetically constrained model, we focus on the known property that equilibrium dynamics take place at a first-order dynamical phase transition point in the space of time-realizations. We investigate the finite-size properties of this first order transition. By discussing and exploiting a mapping of the classical dynamical transition -an argued glassiness signature- to a first-order quantum transition, we show that the quantum analogy can be exploited to extract finite-size properties, which in many respects are similar to those in genuine mean-field quantum systems with a first-order transition. We fully characterize the finite-size properties of the order parameter across the first order transition.

*Naoko Nakagawa,
Universal expression for adiabatic pumping in terms of nonequilibrium steady states,
Physical Review E 90, 022108/1-6 (2014).

[Summary] We develop a unified treatment of pumping and nonequilibrium thermodynamics. We show that the pumping current generated through an adiabatic mechanical operation in equilibrium can be expressed in terms of the stationary distribution of the corresponding driven nonequilibrium system. We also show that the total transfer in pumping can be evaluated from the work imported to the driven counterpart. These findings lead us to a unified viewpoint for pumping and nonequilibrium thermodynamics.

*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 experiment. 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.

*Hiroki Ohta and Shin-ichi Sasa,
Jamming transition in kinetically constrained models with the parity symmetry,
Journal of Statistical Physics 155, 827-842 (2014).

[Summary] A class of kinetically constrained models with reflection symmetry is proposed as an extension ofthe Fredrickson-Andersen model. It is proved that the proposed model on the square lattice exhibits a freezingtransition at a non-trivial density. It is conjectured by numerical experiments that the known mechanism of thesingular behaviors near the freezing transition in a previously studied model (spiral model) is not responsiblefor that in the proposed model.

Masato Itami and Shin-ichi Sasa,
Macroscopically measurable force induced by temperature discontinuities at solid-gas interfaces,
Physical Review E 89, 052106/1-6 (2014).

[Summary] We consider a freely movable solid that separates a long tube into two regions, each of which isfilled with a dilute gas. The gases in each region are initially prepared at the same pressure butdifferent temperatures. Under the assumption that the pressure and temperatures of gas particlesbefore colliding with the solid are kept constant over time, we show that temperature gaps appearingon the solid surface generate a force. We provide a quantitative estimation of the force, which turnsout to be large enough to be observed by a macroscopic measurement.

*Shin-ichi Sasa,
Derivation of hydrodynamics from the Hamiltonian description of particle systems,
Physical Review Letters 112, 100602 (2014).

[Summary] Hamiltonian particle systems may exhibit non-linear hydrodynamic phenomena as the time evolution of the density fields of energy, momentum, and mass. In this Letter, an exact equation describing the time evolution is derived assuming the local Gibbs distribution at initial time. The key concept in the derivation is an identity similar to the fluctuation theorems. The Navier-Stokes equation is obtained as a result of simple perturbation expansions in a small parameter that represents the scale separation.

*Takahiro Nemoto, and Shin-ichi Sasa,
Computation of large deviation statistics via iterative measurement-and-feedback procedure,
Physical Review Letters 112, 090602/1-5 (2014).

[Summary] We propose a computational method for large deviation statistics of time-averaged quantities in general Markov processes. In our proposed method, we repeat a response measurement against external forces, where the forces are determined by the previous measurement as a feedback. Consequently, we obtain a set of stationary states corresponding to an exponential family of distributions, each of which shows rare events in the original system as the typical behavior. As a demonstration of our method, we study large deviation statistics of one-dimensional lattice gas models.

*Masahito Ueda and Shin-ichi Sasa,
Calculation of 1RSB transition temperature of spin glass models on regular random graphs under the replica symmetric ansatz,
Journal of Statistical Mechanics: Theory and Experiment P02005/1-21 (2014).

[Summary] We study p-spin glass models on regular random graphs.By analyzing the Franz-Parisi potential with a two-body cavity field approximation under the replica symmetric ansatz, we obtain a good approximation of the 1RSB transition temperature for $p=3$. Our calculation method is much easier than the 1RSB cavity method because the result is obtained by solving self-consistent equations with Newton's method.

*Shin-ichi Sasa,
Possible extended forms of thermodynamic entropy,
Journal of Statistical Mechanics: Theory and Experiment , P01004/1-16 (2014).

[Summary] Thermodynamic entropy is determined by a heat measurement through the Clausius equality. The entropy then formalizesa fundamental limitation of operations by the second lawof thermodynamics. The entropy is also expressed as the Shannon entropy of the microscopic degrees of freedom. Whenever an extension of thermodynamic entropy is attempted,we must pay special attention to how its three different aspects just mentioned are altered. In this paper, we discuss possible extensions of the thermodynamic entropy.

Johannes-Geert Hagmann, Naoko Nakagawa, and *Michel Peyrard,
Characterization of the low-temperature properties of a simplified protein model,
Physical Review E 89, 012705/1-13 (2014).

[Summary] Prompted by results that showed that a simple protein model, the frustrated Go ̄ model, appears to exhibit a transition reminiscent of the protein dynamical transition, we examine the validity of this model to describe the low-temperature properties of proteins. First, we examine equilibrium fluctuations. We calculate its incoherent neutron-scattering structure factor and show that it can be well described by a theory using the one-phonon approximation. By performing an inherent structure analysis, we assess the transitions among energy states at low temperatures. Then, we examine nonequilibrium fluctuations after a sudden cooling of the protein. We investigate the violation of the fluctuation-dissipation theorem in order to analyze the protein glass transition. We find that the effective temperature of the quenched protein deviates from the temperature of the thermostat, however it relaxes towards the actual temperature with an Arrhenius behavior as the waiting time increases. These results of the equilibrium and nonequilibrium studies converge to the conclusion that the apparent dynamical transition of this coarse-grained model cannot be attributed to a glassy behavior.