arXiv subjects

Shin-ichi Sasa

Publications and source records attributed to Shin-ichi Sasa.

At least 73 records · Page 4Linked to original sources

arXiv2018

Entropic bounds on currents in Langevin systems

We derive a bound on generalized currents for Langevin systems in terms of the total entropy production in the system and its environment. For overdamped dynamics, any generalized current is bounded by the total rate of entropy production. We show that this entropic bound on the magnitude of generalized currents imposes power-efficiency tradeoff relations for ratchets in contact with a heat bath: Maximum efficiency---Carnot efficiency for a Smoluchowski-Feynman ratchet and unity for a flashing or rocking ratchet---can only be reached at vanishing power output. For underdamped dynamics, while there may be reversible currents that are not bounded by the entropy production rate, we show that the output power and heat absorption rate are irreversible currents and thus obey the same bound. As a consequence, a power-efficiency tradeoff relation holds not only for underdamped ratchets but also for periodically driven heat engines. For weak driving, the bound results in additional constraints on the Onsager matrix beyond those imposed by the Second Law. Finally, we discuss the connection between heat and entropy in a non-thermal situation where the friction and noise intensity are state-dependent.

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arXiv2017

Liquid-gas transitions in steady heat conduction

We study liquid-gas transitions of heat conduction systems in contact with two heat baths under constant pressure in the linear response regime. On the basis of local equilibrium thermodynamics, we propose an equality with a global temperature, which determines the volume near the equilibrium liquid-gas transition. We find that the formation of the liquid-gas interface is accompanied by a discontinuous change in the volume when increasing the mean temperature of the baths. A super-cooled gas near the interface is observed as a stable steady state.

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arXiv2017

The most effective model for describing the universal behavior of unstable surface growth

We study a noisy Kuramoto-Sivashinsky (KS) equation which describes unstable surface growth and chemical turbulence. It has been conjectured that the universal long-wavelength behavior of the equation, which is characterized by scale-dependent parameters, is described by a Kardar-Parisi-Zhang (KPZ) equation. We consider this conjecture by analyzing a renormalization-group equation for a class of generalized KPZ equations. We then uniquely determine the parameter values of the KPZ equation that most effectively describes the universal long-wavelength behavior of the noisy KS equation.

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arXiv2017

Replica symmetry breaking in trajectory space for the trap model

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.

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arXiv2017

Universal Form of Stochastic Evolution for Slow Variables in Equilibrium Systems

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.

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arXiv2016

Nonequilibrium fluctuation response relation in a time scale separated system

We present a theoretical framework to analyze the violation of fluctuation-response relation (FRR) for any observable from a finite Markov system with two well-separated time scales. We find that, generally for both slow and fast observables, a broad plateau exists in the intermediate frequency region, which contributes to a finite hidden entropy production. Assuming that non-equilibrium behavior arises only from coupling of slow and fast processes, we find that, at large observation time scae, the effective temperature for a slow observable deviates only slightly from the bath temperature, accompanied by an emerging well-defined effective potential landscape, while the deviation is significant for a fast observable. Our study also identifies a wider range of applicability of the Harada-Sasa equality in Markov jumping systems.

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arXiv2016

Gaussian white noise as a resource for microscopic engines

We show that uncorrelated Gaussian noise, despite its paradigmatic association with thermal equilibrium, can drive a system out of equilibrium and can serve as a resource from which work can be extracted. We consider an overdamped particle in a periodic potential with an internal degree of freedom and a state-dependent friction, coupled to an equilibrium bath. Applying additional Gaussian white noise drives the system into a non-equilibrium steady state and causes a finite current if the potential is spatially asymmetric. We calculate the current explicitly in the three complementary limits. Since the particle current is driven solely by additive Gaussian white noise, this shows that the latter can potentially be exploited as a work resource to power small engines. By comparing the extracted power to the energy injection due to the noise, we find an expression for the efficiency of such an engine.

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arXiv2016

Entropy production of nano systems with timescale separation

Energy flow in bio-molecular 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 timescale 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 timescale. Our findings suggest a general possibility to probe hidden entropy production in nano systems without direct observation of fast variables.

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arXiv2016

Thermodynamic entropy as a Noether invariant

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 non-uniform time translation $t\to t+η\hbar β$, where $η$ is a small parameter, $\hbar$ 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 quasi-static processes in thermodynamics.

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arXiv2015

Replica symmetry breaking in trajectories of a driven Brownian particle

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 to the canonical ensemble of directed polymers.

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arXiv2015

Derivation of Stokes' Law from Kirkwood's Formula and the Green-Kubo Formula via Large Deviation Theory

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.

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arXiv2015

Finite size effects in a mean-field kinetically constrained model: dynamical glassiness and quantum criticality

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.

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arXiv2015

Nonequilibrium Statistical Mechanics for Adiabatic Piston Problem

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 $ε\equiv\sqrt{m/M}$, we calculate the steady velocity up to order $ε$.

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arXiv2014

Collective Dynamics from Stochastic Thermodynamics

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.

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arXiv2014

Exact equalities and thermodynamic relations for nonequilibrium steady states

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.

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arXiv2014

Macroscopically measurable force induced by temperature discontinuities at solid-gas interfaces

We consider a freely movable solid that separates a long tube into two regions, each of which is filled with a dilute gas. The gases in each region are initially prepared at the same pressure but different temperatures. Under the assumption that the pressure and temperatures of gas particles before colliding with the solid are kept constant over time, we show that temperature gaps appearing on the solid surface generate a force. We provide a quantitative estimation of the force, which turns out to be large enough to be observed by a macroscopic measurement.

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arXiv2014

Jamming transition in kinetically constrained models with reflection symmetry

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

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arXiv2014

Nonequilibrium dissipation-free transport in F1-ATPase and the thermodynamic role of asymmetric allosterism

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.

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