Nonlinear thermodynamic quantum master equation: Properties and examples

TL;DR

This paper explores the nonlinear properties of a thermodynamic quantum master equation, demonstrating its implications for equilibrium states, low-temperature validity, and challenges in quantum dynamics modeling.

Contribution

It introduces a nonlinear thermodynamic quantum master equation, analyzes its properties, and provides solution strategies with practical examples, extending understanding of quantum thermodynamics.

Findings

The nonlinear equation naturally yields canonical equilibrium states.

It extends the validity of quantum descriptions to lower temperatures.

The approach highlights conceptual issues like the absence of a Heisenberg picture.

Abstract

The quantum master equation obtained from two different thermodynamic arguments is seriously nonlinear. We argue that, for quantum systems, nonlinearity occurs naturally in the step from reversible to irreversible equations and we analyze the nature and consequences of the nonlinear contribution. The thermodynamic nonlinearity naturally leads to canonical equilibrium solutions and extends the range of validity to lower temperatures. We discuss the Markovian character of the thermodynamic quantum master equation and introduce a solution strategy based on coupled evolution equations for the eigenstates and eigenvalues of the density matrix. The general ideas are illustrated for the two-level system and for the damped harmonic oscillator. Several conceptual implications of the nonlinearity of the thermodynamic quantum master equation are pointed out, including the absence of a Heisenberg picture and the resulting difficulties with defining multi-time correlations.