Nonequilibrium steady states in Langevin thermal systems (original) (raw)
Related papers
Fluctuation-Dissipation Theorem and Detailed Balance in Langevin Systems
arXiv: Statistical Mechanics, 2016
Equilibrium is characterized by its fundamental properties such as the fluctuation-dissipation theorem, the detailed balance, and no heat dissipation. Based on the stochastic thermodynamics, we show that these three properties are equivalent to each other in conventional Langevin systems with microscopic reversibility. In the presence of velocity-dependent forces breaking the microscopic reversibility, we prove that the fluctuation-dissipation theorem and the detailed balance mutually exclude each other and no equivalence relation is possible between any two of the three properties. This implies that a nonequilibrium steady state with velocity-dependent forces may share some equilibrium properties but not all of them, in contrast that it can not share any of them without velocity-dependent forces. Our results are illustrated with a few example systems.
Steady-State Thermodynamics of Langevin Systems
Physical Review Letters, 2001
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. 130, 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.
Physical review. E, Statistical, nonlinear, and soft matter physics, 2006
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 d...
PHYSICAL REVIEW RESEARCH 4, 043125 (2022), 2022
We construct a unified theory of thermodynamics and stochastic thermodynamics for classical nonequilibrium systems driven by non-conservative forces, using the recently developed covariant Ito-Langevin theory. The thermodynamic forces are split into a conservative part and a non-conservative part. Thermodynamic functions are defined using the reference conservative system. Work and heat are partitioned into excess parts and house-keeping parts, which are due to, respectively, conservative forces and non-conservative forces. Excess entropy production (EP) and house-keeping EP are analogously defined. The splitting of thermodynamic forces is subjected to an arbitrariness resembling a gauge symmetry, with each gauge defining a reference conservative Langevin system. In the special Gibbs gauge, the nonequilibrium steady state (NESS) is characterized by Gibbs canonical distribution, the excess heat agrees with that defined by Hatano and Sasa, and the excess EP agrees with that of Glansdorff and Prigogine, i.e., it is the time rate of the second-order variation of system entropy near the NESS. Adopting the Gibbs gauge, and focusing on the excess parts of thermodynamic quantities, a complete analogy between thermodynamics of non-conservative systems and that of conservative systems is established. One important consequence of this analogy is that both the free energy and excess EP are minimized at NESS. Our theory therefore constitutes a statistical foundation both for the steady-state thermodynamics theory due to Sasa and Tasaki and for the stability theory of NESS due to Glansdorff and Prigogine. These results are valid even if the system is far from equilibrium. By studying detailed fluctuation theorem, we find striking differences between systems with symmetric kinetic matrices and those with asymmetric kinetic matrices. For systems with asymmetric kinetic matrices, the total EP is the sum of house-keeping EP, excess EP, and pumped entropy. Entropy pumping is an exchange of entropy between the system and environment without necessarily involving dissipation. In the presence of entropy pumping, the system may behave as either a demon or an antidemon. Fluctuation theorems and work relations are derived both for total work and for excess work. For systems with symmetric kinetic matrices, there is no entropy pumping, yet in the Gibbs gauge, the excess work and house-keeping work each satisfies a separate fluctuation theorem. We illustrate our theory using many concrete examples.
Langevin Equation and Thermodynamics
Progress of Theoretical Physics Supplement, 1998
We introduce a framework of energetics into the stochastic dynamics described by Langevin equation in which fluctuation force obeys the Einstein relation. The energy conservation holds in the individual realization of stochastic process, while the second law and steady state thermodynamics of Oono and Paniconi [Y. Oono and M. Paniconi, this issue] are obtained as ensemble properties of the process.
Fluctuation theorems for excess and housekeeping heat for underdamped Langevin systems
We present a simple derivation of the integral fluctuation theorems for excess housekeeping heat for an underdamped Langevin system, without using the concept of dual dynamics. In conformity with the earlier results, we find that the fluctuation theorem for housekeeping heat holds when the steady state distributions are symmetric in velocity, whereas there is no such requirement for the excess heat. We first prove the integral fluctuation theorem for the excess heat, and then show that it naturally leads to the integral fluctuation theorem for housekeeping heat. We also derive the modified detailed fluctuation theorems for the excess and housekeeping heats.
Fluctuation properties of steady-state Langevin systems
Physical Review E, 2007
Motivated by stochastic models of climate phenomena, the steady-state of a linear stochastic model with additive Gaussian white noise is studied. Fluctuation theorems for nonequilibrium steady-states provide a constraint on the character of these fluctuations. The properties of the fluctuations which are unconstrained by the fluctuation theorem are investigated and related to the model parameters. The irreversibility of trajectory segments, which satisfies a fluctuation theorem, is used as a measure of nonequilibrium fluctuations. The moments of the irreversibility probability density function (pdf) are found and the pdf is seen to be non-Gaussian. The average irreversibility goes to zero for short and long trajectory segments and has a maximum for some finite segment length, which defines a characteristic timescale of the fluctuations. The initial average irreversibility growth rate is equal to the average entropy production and is related to noise-amplification. For systems with a separation of deterministic timescales, modes with timescales much shorter than the trajectory timespan and whose noise amplitudes are not asymptotically large, do not, to first order, contribute to the irreversibility statistics, providing a potential basis for dimensional reduction.
Physical Review E, 2004
We theoretically study Langevin systems with a tilted periodic potential. It has been known that the ratio Θ of the diffusion constant D to the differential mobility µ d 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. Hence the relation D = µ d Θ among independent measurable quantities D, µ d and Θ can be interpreted as an extension of the Einstein relation.
Physica A-statistical Mechanics and Its Applications, 2007
We investigate the effects of temperature on the properties of the time relaxation to equilibrium and nonequilibrium steady states of correlation functions of some Langevin harmonic systems. We consider commonly used dissipative and conservative Langevin dynamics, and show that the time relaxation rate depends on the temperature in the case of thermal reservoirs at different temperatures connected to the system, but it does not happen in the case of relaxation to equilibrium, i.e., if all the heat bath are at the same temperature. Our formalism maps the initial stochastic problem on a noncanonical quantum field theory, and the calculations of the relaxation rates are based on a perturbative analysis. We argue to show the reliability of the perturbative computation. r
Physical Review X, 2013
Common algorithms for simulating Langevin dynamics are neither statistically time-reversible, nor do they preserve the equilibrium distribution. Instead, even with a time-independent Hamiltonian, finite time step Langevin integrators model a driven, nonequilibrium dynamics that breaks time-reversal symmetry. Herein, we demonstrate that these problems can be resolved with a Langevin integrator that splits the dynamics into separate deterministic and stochastic substeps. This allows the total energy change of a driven system to be divided into heat, work, and pseudo-work -the work induced by the finite time step. The extent of time-symmetry breaking due to the finite time step can be measured and true equilibrium properties recovered.