arXiv subjects

Shin-ichi Sasa

Publications and source records attributed to Shin-ichi Sasa.

At least 127 records · Page 7Linked to original sources

arXiv2006

The law of action and reaction for the effective force in a nonequilibrium colloidal system

We study a nonequilibrium Langevin many-body system containing two 'test' particles and many 'background' particles. The test particles are spatially confined by a harmonic potential, and the background particles are driven by an external driving force. Employing numerical simulations of the model, we formulate an effective description of the two test particles in a nonequilibrium steady state. In particular, we investigate several different definitions of the effective force acting between the test particles. We find that the law of action and reaction does not hold for the total mechanical force exerted by the background particles, but that it does hold for the thermodynamic force defined operationally on the basis of an idea used to extend the first law of thermodynamics to nonequilibrium steady states.

cond-mat.stat-mech↗

arXiv2005

Steady state thermodynamics

The present paper reports our attempt to search for a new universal framework in nonequilibrium physics. We propose a thermodynamic formalism that is expected to apply to a large class of nonequilibrium steady states including a heat conducting fluid, a sheared fluid, and an electrically conducting fluid. We call our theory steady state thermodynamics (SST) after Oono and Paniconi's original proposal. The construction of SST is based on a careful examination of how the basic notions in thermodynamics should be modified in nonequilibrium steady states. We define all thermodynamic quantities through operational procedures which can be (in principle) realized experimentally. Based on SST thus constructed, we make some nontrivial predictions, including an extension of Einstein's formula on density fluctuation, an extension of the minimum work principle, the existence of a new osmotic pressure of a purely nonequilibrium origin, and a shift of coexistence temperature. All these predictions may be checked experimentally to test SST for its quantitative validity.

cond-mat.stat-mech↗

arXiv2005

Energy dissipation and violation of the fluctuation-response relation in non-equilibrium Langevin systems

The fluctuation-response relation is a fundamental relation that is applicable to systems near equilibrium. On the other hand, when a system is driven far from equilibrium, this relation is violated in general because the detailed-balance condition is not satisfied in nonequilibrium systems. Even in this case, it has been found that for a class of Langevin equations, there exists an equality between the extent of violation of the fluctuation-response relation in the nonequilibrium steady state and the rate of energy dissipation from the system into the environment [T. Harada and S. -i. Sasa, Phys. Rev. Lett. 95, 130602 (2005)]. Since this equality involves only experimentally measurable quantities, it serves as a proposition to determine experimentally whether the system can be described by a Langevin equation. Furthermore, the contribution of each degree of freedom to the rate of energy dissipation can be determined based on this equality. In this paper, we present a comprehensive description on this equality, and provide a detailed derivation for various types of models including many-body systems, Brownian motor models, time-dependent systems, and systems with multiple heat reservoirs.

cond-mat.stat-mech↗

arXiv2005

Microscopic description of the equality between violation of fluctuation-dissipation relation and energy dissipation

In systems far from equilibrium, the fluctuation-dissipation relation is violated due to the lack of detailed balance. Recently, for a class of Langevin equations, it has been proved that this violation is related to energy dissipation as an equality [T. Harada and S. Sasa, Phys. Rev. Lett., in press; cond-mat/0502505]. We provide a microscopic description of this equality by studying a non-equilibrium colloidal system on the basis of classical mechanics with some physical assumptions.

cond-mat.stat-mech↗

arXiv2005

Equality connecting energy dissipation with violation of fluctuation-response relation

In systems driven away from equilibrium, the velocity correlation function and the linear response function to a small perturbation force do not satisfy the fluctuation-response relation (FRR) due to the lack of detailed balance in contrast to equilibrium systems. In this Letter, an equality between an extent of the FRR violation and the rate of energy dissipation is proved for Langevin systems under non-equilibrium conditions. This equality enables us to calculate the rate of energy dissipation by quantifying the extent of the FRR violation, which can be measured experimentally.

cond-mat.stat-mech↗

arXiv2005

Anomalous time correlation in two-dimensional driven diffusive systems

We study the time correlation function of a density field in two-dimensional driven diffusive systems within the framework of fluctuating hydrodynamics. It is found that the time correlation exhibits power-law behavior in an intermediate time regime in the case that the fluctuation-dissipation relation is violated and that the power-law exponent depends on the extent of this violation. We obtain this result by employing a renormalization group method to treat a logarithmic divergence in time.

cond-mat.stat-mech↗

arXiv2005

Exact transformation of a Langevin equation to a fluctuating response equation

We demonstrate that a Langevin equation that describes the motion of a Brownian particle under non-equilibrium conditions can be exactly transformed to a special equation that explicitly exhibits the response of the velocity to a time dependent perturbation. This transformation is constructed on the basis of an operator formulation originally used in nonlinear perturbation theory for differential equations by extending it to stochastic analysis. We find that the obtained expression is useful for the calculation of fundamental quantities of the system, and that it provides a physical basis for the decomposition of the forces in the Langevin description into effective driving, dissipative, and random forces in a large-scale description.

cond-mat.stat-mech↗

arXiv2005

Statistics of unstable periodic orbits of a chaotic dynamical system with a large number of degrees of freedom

For a simple model of chaotic dynamical systems with a large number of degrees of freedom, we find that there is an ensemble of unstable periodic orbits (UPOs) with the special property that the expectation values of macroscopic quantities can be calculated using only one UPO sampled from the ensemble. Evidence to support this conclusion is obtained by generating the ensemble by Monte Carlo calculation for a statistical mechanical model described by a space-time Hamiltonian that is expressed in terms of Floquet exponents of UPOs. This result allows us to interpret the recent interesting discovery that statistical properties of turbulence can be obtained from only one UPO [G. Kawahara and S. Kida, J. Fluid Mech. {\bf 449}, 291 (2001); S. Kato and M. Yamada, Phys. Rev. E {\bf 68}, 025302(R)(2003)].

nlin.CD↗

arXiv2005

Extended Einstein relations with a complex effective temperature in a one dimensional driven lattice gas

We carried out numerical experiments on a one-dimensional driven lattice gas to elucidate the statistical properties of steady states far from equilibrium. By measuring the bulk density diffusion constant $D$, the conductivity $σ$, the intensity of density fluctuations $χ$, we confirm that the Einstein relation $Dχ=σT$, which is valid in the linear response regime about equilibrium, does not hold in such steady states. Here, $T$ is the environment temperature, and the Boltzmann constant is set to unity. Recalling that the Einstein relation provided the first step in the construction of linear response theory, we attempt to extend it to a generalized form valid in steady states far from equilibrium. In order to obtain new relations among measurable quantities, we define a complex effective temperature $Θ-iΦ$ from studying the static response of the system to a slowly varying potential in space. Replacing $T$ in the Einstein relation by the real part of the effective temperature $Θ$, we numerically confirm that the relation $Dχ=σΘ$ holds in the nonequilibrium steady states far from equilibrium that we study. In addition to this extended form, we find the new relation $(L/2π)cχ=σΦ$, where $c$ represents the propagation velocity of density fluctuations.

cond-mat.stat-mech↗

arXiv2004

Decomposition of force fluctuations far from equilibrium

By studying a nonequilibrium Langevin system, we find that a simple condition determines the decomposition of the coarse-grained force into a dissipative force, an effective driving force and noise. From this condition, we derive a new universal inequality, $D \ge γ\mud^2 T$, relating the diffusion constant $D$, the differential mobility $\mud$, the bare friction constant $γ$ and the temperature $T$. Due to the general nature of the argument we present, we believe that our idea concerning this decomposition can be applied to a wide class of systems far from equilibrium.

cond-mat.stat-mech↗

arXiv2004

Long range spatial correlation between two Brownian particles under external driving

We study the large distance behavior of a steady distribution of two Brownian particles under external driving in a two-dimensional space. Employing a method of perturbative system reduction, we analyze a Fokker-Planck equation that describes the time evolution of the probability density for the two particles. The expression we obtain shows that there exist a long range correlation between the two particles, of $1/r^2$ type.

cond-mat.stat-mech↗

arXiv2004

Effective temperature in nonequilibrium steady states of Langevin systems with a tilted periodic potential

We theoretically study Langevin systems with a tilted periodic potential. It has been known that the ratio $Θ$ of the diffusion constant to the differential mobility is not equal to the temperature of the environment (multiplied by the Boltzmann constant), except in the linear response regime, where the fluctuation dissipation theorem holds. In order to elucidate the physical meaning of $Θ$ far from equilibrium, we analyze a modulated system with a slowly varying potential. We derive a large scale description of the probability density for the modulated system by use of a perturbation method. The expressions we obtain show that $Θ$ plays the role of the temperature in the large scale description of the system and that $Θ$ can be determined directly in experiments, without measurements of the diffusion constant and the differential mobility.

cond-mat.stat-mech↗

arXiv2003

Thermodynamic relations in a driven lattice gas: numerical exprements

We explore thermodynamic relations in non-equilibrium steady states with numerical experiments on a driven lattice gas. After operationally defining the pressure and chemical potential in the driven lattice gas, we confirm numerically the validity of the integrability condition (the Maxwell relation) for the two quantities whose values differ from those for an equilibrium system. This implies that a free energy function can be constructed for the non-equilibrium steady state that we consider. We also investigate a fluctuation relation associated with this free energy function. Our result suggests that the compressibility can be expressed in terms of density fluctuations even in non-equilibrium steady states.

cond-mat.stat-mech↗

arXiv2003

Anomalous Pressure in Fluctuating Shear Flow

We investigate how the pressure in fluctuating shear flow depends on the shear rate $S$ and on the system size $L$ by studying fluctuating hydrodynamics under shear conditions. We derive anomalous forms of the pressure for two limiting values of the dimensionless parameter $λ=SL^2/ν$, where $ν$ is the kinematic viscosity. In the case $λ\ll 1$, the pressure is not an intensive quantity because of the influence of the long-range spatial correlations of momentum fluctuations. In the other limit $λ\gg 1$, the long-range correlations are suppressed at large distances, and the pressure is intensive. In this case, however, there is the interesting effect that the non-equilibrium correction to the pressure is proportional to $S^{3/2}$, which was previously obtained with the projection operator method [K. Kawasaki and J. D. Gunton, Phys. Rev. {\bf A 8}, 2048, (1973)].

cond-mat.stat-mech↗

arXiv2002

Steady state thermodynamics for heat conduction

Following the proposal of steady state thermodynamics (SST) by Oono and Paniconi, we develop a phenomenological theory for steady nonequilibrium states in systems with heat conduction. We find that there is essentially a unique consistent thermodynamics, and make concrete predictions, i.e, the existence of a new osmotic pressure and a shift in the coexistence temperature. These predictions allow one to test for the quantitative validity of SST by comparing them with experiments.

cond-mat.stat-mech↗

arXiv2000

Steady State Thermodynamics of Langevin Systems

We study Langevin dynamics describing nonequilibirum steady states. Employing the phenomenological framework of steady state thermodynamics constructed by Oono and Paniconi [Prog. Theor. Phys. Suppl. {\bf130}, 29 (1998)], we find that the extended form of the second law which they proposed holds for transitions between steady states and that the Shannon entropy difference is related to the excess heat produced in an infinitely slow operation. A generalized version of the Jarzynski work relation plays an important role in our theory.

cond-mat.stat-mech↗

arXiv2000

A fluctuation theorem for phase turbulence of chemical oscillatory waves

Through numerical simulations of the Kuramoto equation, which displays high-dimensional dissipative chaos, we find a quantity representing the cost for maintenance of a spatially non-uniform structure that appears in the phase turbulence of chemical oscillatory waves. We call this quantity the generalized entropy production and demonstrate that its distribution function possesses a symmetry expressed by a fluctuation theorem. We also report a numerical result which suggests a relation between this generalized entropy production rate and the Kolmogorov-Sinai entropy.

nlin.CD↗

arXiv2000

A non-equilibrium equality in Hamiltonian chaos

We numerically study a billiard system with a time-dependent force, and our results suggest the existence of a limitation on possible transitions between steady states in Hamiltonian chaos, in analogy to the limitation on transitions between equilibrium states described by the second law of thermodynamics. This limitation is expressed in terms of irreversible information loss, which is defined for each trajectory through Lyapunov analysis. As a key step in the study, we demonstrate a non-equilibrium equality which means that the average of the inverse exponential of the irreversible information loss is unity, where the average is taken over initial conditions sampled from the microcanonical ensemble.

nlin.CD↗