Thermodynamically consistent master equation based on subsystem eigenstates

TL;DR

This paper introduces a thermodynamically consistent local master equation for many-body quantum systems with subsystems coupled to thermal baths, addressing inconsistencies in previous models and validated through a two-qubit heat transfer example.

Contribution

The authors develop a new local master equation using subsystem eigenstates and secular approximation to ensure thermodynamic consistency in systems with intersubsystem interactions.

Findings

Violations of thermodynamic laws are avoided with the new approach

The modified master equation accurately describes two-qubit heat transfer

The method improves the physical consistency of local quantum master equations

Abstract

Master equations under appropriate assumptions are efficient tools for the study of open quantum systems. For many-body systems, subsystems of which locally couple to thermal baths and weakly interact with each other, the local approach provides a more convenient description than the global approach. However, these local master equations are believed to generate inconsistencies with the laws of thermodynamics when intersubsystem interactions exist. Here we develop an alternative local master equation by virtue of similar approximations used in deriving the traditional Gorini-Kossakowski-Lindblad-Sudarshan master equation. In particular, we stick to using eigenstates of each subsystem to construct quantum jump operators, and the secular approximation is also employed to modify the intersubsystem interactions. Our results show that violations of thermodynamic laws will be avoided after correcting intersubsystem interactions. Finally, We study a two-qubit heat transfer model and this further shows the validity of our modified master equation.