Open system dynamics from thermodynamic compatibility

TL;DR

This paper characterizes the general form of quantum Markovian master equations compatible with thermodynamic principles, providing a framework to assess the thermodynamic consistency of various derivations and approximations in open quantum systems.

Contribution

It derives the general structure of thermodynamically compatible quantum master equations using spectral analysis, clarifying conditions for their validity and implications for open system dynamics.

Findings

Global master equations are thermodynamically compatible.

The secular approximation's validity is clarified.

No exceptional points exist in thermodynamically consistent open system dynamics.

Abstract

Thermodynamics entails a set of mathematical conditions on quantum Markovian dynamics. In particular, strict energy conservation between the system and environment implies that the dissipative dynamical map commutes with the unitary system propagator. Employing spectral analysis we prove the general form of the ensuing master equation. We compare this result to master equations obtained from standard microscopic derivations. The obtained formal structure can be employed to test the compatibility of approximate derivations with thermodynamics. For example, it designates that global master equations are the compatible choice. The axiomatic approach sheds light on the validity of the secular approximation in microscopic derivations, the form of the steady state in heat transport phenomena, and indicates the lack of exceptional points in the dynamics of open quantum systems.