A Nonlinear Master Equation for Open Quantum Systems

TL;DR

This paper introduces a nonlinear master equation for open quantum systems that accurately captures entropy and equilibrium states, unifying quantum thermodynamics with stochastic dynamics.

Contribution

It derives a nonlinear quantum master equation with an exact Gibbs equilibrium, linking quantum entropy, Wigner functions, and stochastic Langevin-Bohm dynamics.

Findings

Equilibrium solution is the canonical Gibbs density matrix.

The nonlinear equation accounts for thermo-quantum entropy.

Reduces to the Smoluchowski-Bohm equation at large friction.

Abstract

A nonlinear master equation is derived, reflecting properly the entropy of open quantum systems. In contrast to linear alternatives, its equilibrium solution is exactly the canonical Gibbs density matrix. The corresponding nonlinear equation for the Wigner function accounts rigorously for the thermo-quantum entropy. It reduces at large friction to the Smoluchowski-Bohm equation in the coordinate subspace, which reflects the stochastic Langevin-Bohm dynamics. The previously derived Maxwell-Heisenberg relation for the nonequilibrium momentum dispersion of quantum Brownian particles is confirmed as well as the related quantum generalization of the classical Einstein law of Brownian motion.