Equilibrium and transient thermodynamics: A unified dissipaton-space approach

TL;DR

This paper introduces a unified dissipaton-equation-of-motion (DEOM) framework for analyzing both equilibrium and transient thermodynamics in open quantum systems, combining imaginary-time and real-time formalisms for comprehensive thermodynamic insights.

Contribution

The work develops a unified DEOM approach that integrates equilibrium and nonequilibrium thermodynamics, including an analytical continuation for imaginary-time formalism and a thermodynamic integral formalism.

Findings

Numerical results on a spin-boson system demonstrate the method's effectiveness.

The approach reveals anharmonic features and entropy relations in quantum systems.

Indications of solvent-cage formation are observed in the simulations.

Abstract

This work presents a unified dissipaton-equation-of-motion (DEOM) theory and its evaluations on the Helmholtz free energy change due to the isotherm mixing of two isolated subsystems. One is a local impurity and another is a nonlocal Gaussian bath. DEOM constitutes a fundamental theory for such open quantum mixtures. To complete the theory, we construct also the imaginary-time DEOM formalism via an analytical continuation of dissipaton algebra, which would be limited to equilibrium thermodynamics. On the other hand, the real-time DEOM deals with both equilibrium structural and nonequilibrium dynamic properties. Its combination with the thermodynamic integral formalism would be a viable and accurate means to both equilibrium and transient thermodynamics. As illustrations, we report the numerical results on a spin--boson system, with elaborations on the underlying anharmonic features, the thermodynamic entropy versus the von Neumann entropy, and an indication of "solvent-cage" formation. Beside the required asymptotic equilibrium properties, the proposed transient thermodynamics also supports the basic spontaneity criterion.