The entropy production of thermal operations

TL;DR

This paper explores how a recent redefinition of heat impacts the expression of entropy production in thermal operations, revealing that under certain conditions, entropy production equals the mutual information between system and bath.

Contribution

It introduces a new expression for entropy production based on a redefinition of heat, linking it to mutual information in thermal operations.

Findings

Entropy production equals mutual information when initial states are factorized.

Thermal operations cannot generate quantum correlations if the initial state is energy-diagonal.

The new entropy production expression aligns with the preservation of total entropy.

Abstract

According to the first and second laws of thermodynamics and the definitions of work and heat, microscopic expressions for the non-equilibrium entropy production have been achieved. Recently, a redefinition of heat has been presented in [\href{Nature Communicationsvolume 8, Article number: 2180 (2017)}{Nat. Commun. 8, 2180 (2017)}]. We are going to determine how this redefinition of heat could affect the expression of the entropy production. Utilizing this new definition of heat, it could be found out that there is a new expression for the entropy production for thermal operations. It could be derived if the initial state of the system and the bath is factorized, and if the total entropy of composite system is preserved, then the new entropy production will be equal to mutual information between the system and the bath. It is shown that if the initial state of the system is diagonal in energy bases, then the thermal operations cannot create a quantum correlation between the system and the bath.