Entropy production in a non-Markovian environment

TL;DR

This paper investigates entropy production in non-Markovian open systems, deriving modified fluctuation relations that account for environment correlations, with a specific example of an overheated single electron box.

Contribution

It introduces a non-Markovian model for open system dynamics and derives new fluctuation relations incorporating environment-induced correlations.

Findings

Derived non-Markovian entropy production term.

Established modified fluctuation relations for non-Markovian systems.

Applied the theory to an overheated single electron box.

Abstract

Stochastic thermodynamics and the associated fluctuation relations provide the means to extend the fundamental laws of thermodynamics to small scales and systems out of equilibrium. The fluctuating thermodynamic variables are usually treated in the context of either isolated Hamiltonian evolution, or Markovian dynamics in open systems. However, there is no reason a priori why the Markovian approximation should be valid in driven systems under non-equilibrium conditions. In this work we introduce an explicitly non-Markovian model of dynamics of an open system, where the correlations between the system and the environment drive a subset of the environment out of equilibrium. Such a an environment gives rise to a new type of non-Markovian entropy production term. Such non-Markovian components must be taken into account in order to recover the fluctuation relations for entropy. As a concrete example, we explicitly derive such modified fluctuation relations for the case of an overheated single electron box.