Quantum mechanics of open systems: Dissipaton theories

TL;DR

This paper reviews the development of dissipaton theories for quantum open systems, highlighting their physical basis, algebraic structure, and applications to thermodynamics, including equilibrium and nonequilibrium processes.

Contribution

It introduces a comprehensive framework of dissipaton theories, including phase-space algebra and DEOM formulations, advancing the quantum mechanics of open systems.

Findings

Accurate numerical reproduction of Jarzynski equality and Crooks relation.

Development of dissipaton theories for thermodynamic mixing processes.

Unified DEOM-space formulations for different quantum pictures.

Abstract

This Perspective presents a comprehensive account of the dissipaton theories developed in our group since 2014, including the physical picture of dissipatons and the phase-space dissipaton algebra. The dissipaton-equation-of-motion-space (DEOM-space) formulations cover the Schr\"odinger picture, the Heisenberg picture, and further the imaginary-time DEOM. Recently developed are also the dissipaton theories for studying equilibrium and nonequilibrium thermodynamic mixing processes. The Jarzynski equality and Crooks relation are accurately reproduced numerically. It is anticipated that dissipaton theories would remain essential towards a maturation of quantum mechanics of open systems.