Stochastic entropy production arising from nonstationary thermal transport

Abstract

We compute statistical properties of the stochastic entropy production associated with the nonstationary transport of heat through a system coupled to a time dependent nonisothermal heat bath. We study the 1-d stochastic evolution of a bound particle in such an environment by solving the appropriate Langevin equation numerically, and by using an approximate analytic solution to the Kramers equation to determine the behaviour of an ensemble of systems. We express the total stochastic entropy production in terms of a relaxational or nonadiabatic part together with two components of housekeeping entropy production and determine the distributions for each, demonstrating the importance of all three contributions for this system. We compare the results with an approximate analytic model of the mean behaviour and we further demonstrate that the total entropy production and the relaxational component approximately satisfy detailed fluctuation relations for certain time intervals. Finally, we comment on the resemblance between the procedure for solving the Kramers equation and a constrained extremisation, with respect to the probability density function, of the spatial density of the mean rate of production of stochastic entropy.

References in corpus (4)

• Fluctuation theorems for stochastic dynamics
• Path-integral analysis of fluctuation theorems for general Langevin processes
• Thermodynamics of Micro- and Nano-Systems Driven by Periodic Temperature Variations
• Work relations for a system governed by Tsallis statistics

Cited by in corpus (14)

• Multiple-scale stochastic processes: decimation, averaging and beyond
• Functionals in stochastic thermodynamics: how to interpret stochastic integrals
• Energy transport between heat baths with oscillating temperatures
• Martingale structure for general thermodynamic functionals of diffusion processes under second-order averaging
• Temperature response in nonequilibrium stochastic systems
• Thermal response of nonequilibrium RC-circuits
• Estimating entropy production in a stochastic system with odd-parity variables
• Stochastic entropy production for continuous measurements of an open quantum system
• Entropy Anomaly in Langevin-Kramers Dynamics with a Temperature Gradient, Matrix Drag, and Magnetic Field
• Stochastic entropy production associated with quantum measurement in a framework of Markovian quantum state diffusion
• Heat Transport Hysteresis Generated through Frequency Switching of a Time-Dependent Temperature Gradient
• Neuromorphic heat transport effects in a molecular junction
• 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