Entropy production from stochastic dynamics in discrete full phase space

Abstract

The stochastic entropy generated during the evolution of a system interacting with an environment may be separated into three components, but only two of these have a non-negative mean. The third component of entropy production is associated with the relaxation of the system probability distribution towards a stationary state and with nonequilibrium constraints within the dynamics that break detailed balance. It exists when at least some of the coordinates of the system phase space change sign under time reversal, and when the stationary state is asymmetric in these coordinates. We illustrate the various components of entropy production, both in detail for particular trajectories and in the mean, using simple systems defined on a discrete phase space of spatial and velocity coordinates. These models capture features of the drift and diffusion of a particle in a physical system, including the processes of injection and removal and the effect of a temperature gradient. The examples demonstrate how entropy production in stochastic thermodynamics depends on the detail that is included in a model of the dynamics of a process. Entropy production from such a perspective is a measure of the failure of such models to meet Loschmidt's expectation of dynamic reversibility.

References in corpus (5)

• Fluctuation theorems for stochastic dynamics
• Path-integral analysis of fluctuation theorems for general Langevin processes
• Integral fluctuation theorem for the housekeeping heat
• Entropy production in full phase space for continuous stochastic dynamics
• Non-equilibrium thermodynamics of stochastic systems with odd and even variables

Cited by in corpus (16)

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• Entropy production in linear Langevin systems
• Heat fluctuations and initial ensembles
• Stochastic entropy production arising from nonstationary thermal transport
• Dependence of integrated, instantaneous, and fluctuating entropy production on the initial state in quantum and classical processes
• Irreversibility at zero temperature from the perspective of the environemnt
• Housekeeping Entropy in Continuous Stochastic Dynamics with Odd-Parity Variables
• Stochastic thermodynamics with odd controlling parameters
• Fluctuation theorems for excess and housekeeping heats for underdamped systems
• Maxwell's demon and the management of ignorance in stochastic thermodynamics
• Generalized free energy and excess/housekeeping decomposition in nonequilibrium systems: from large deviations to thermodynamic speed limits
• Maximum entropy principle for stationary states underpinned by stochastic thermodynamics
• Characterising quantum measurement through environmental stochastic entropy production in a two spin 1/2 system