The geometry and thermodynamics of dissipative quantum systems

TL;DR

This paper introduces a geometric framework for dissipative quantum systems using Dirac's classical analogy, leading to a nonlinear quantum master equation that effectively models complex environments.

Contribution

It develops a novel geometric approach to dissipative quantum mechanics based on commutators and canonical correlations, extending thermodynamics to quantum systems.

Findings

Formulation of a nonlinear quantum master equation

Effective modeling of complex classical environments

Integration of geometric structures into quantum thermodynamics

Abstract

Dirac's method of classical analogy is employed to incorporate quantum degrees of freedom into modern nonequilibrium thermodynamics. The proposed formulation of dissipative quantum mechanics builds entirely upon the geometric structures implied by commutators and canonical correlations. A lucid formulation of a nonlinear quantum master equation follows from the thermodynamic structure. Complex classical environments with internal structure can be handled readily.