Correlations, operations and the second law of thermodynamics

TL;DR

This paper investigates how correlations affect the description of quantum and classical system dynamics in the context of the second law of thermodynamics, proposing a corrected approach for correlated states.

Contribution

It introduces a method to properly describe the dynamics of correlated systems and extends the classical second law to correlated probability distributions.

Findings

Correlations can invalidate standard descriptions of system dynamics.

A new prescription corrects the dynamics of correlated systems.

The classical second law is generalized for correlated probability distributions.

Abstract

Completely positive trace preserving maps are essential for the formulation of the second law of thermodynamics. The dynamics of quantum systems, correlated with their environments, are in general not described by such maps. We explore how this issue can be fixed by describing the classical analogue of this problem. We consider correlated probability distributions, whose subsequent system dynamics is ill-described by stochastic maps, and prescribe the correct way to describe the dynamics. We use this prescription to discuss the classical version of the second law, valid for correlated probability distributions.