Non-Markovianity, entropy production, and Jarzynski equality

TL;DR

This paper investigates how non-Markovian memory effects influence entropy production and information exchange during work protocols, confirming the Jarzynski Equality and revealing the role of memory as an information pump, with non-linearity affecting entropy generation.

Contribution

It demonstrates the Jarzynski Equality holds in non-Markovian systems and uncovers the memory function's role as an information pump, highlighting differences between harmonic and non-harmonic models.

Findings

Jarzynski Equality holds for both harmonic and non-harmonic models.

Memory acts as an information pump, recovering information lost to the reservoir.

Harmonic models do not produce entropy, while non-linearity restores entropy production.

Abstract

We explore the role a non-Markovian memory kernel plays on information exchange and entropy production in the context of a external work protocol. The Jarzynski Equality is shown to hold for both the harmonic and the non-harmonic models. We observe the memory function acts as an information pump, recovering part of the information lost to the thermal reservoir as a consequence of the non-equilibrium work protocol. The pumping action occurs for both the harmonic and non-harmonic cases. Unexpectedly, we found that the harmonic model does not produce entropy, regardless of the work protocol. The presence of even a small amount of non-linearity recovers the more normal entropy producing behaviour, for out-of-equilibrium protocols.