Equilibrium and transient thermodynamics: A unified dissipaton-space approach

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.

10 pages, 2 figures

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• Nonequilibrium work distributions in quantum impurity system-bath mixing processes
• Dissipatons as generalized Brownian particles for open quantum systems: Dissipaton-embedded quantum master equation
• Theoretical formulations on thermodynamics of quantum impurity systems
• Numerical computation of the equilibrium-reduced density matrix for strongly coupled open quantum systems
• Multimode Brownian oscillators: Exact solutions to heat transport
• Numerically "exact" charge transport dynamics in a dissipative electron-phonon model rationalizing the success of the transient localization scenario