Weak invariants, temporally-local equilibria, and isoenergetic processes described by the Lindblad equation

TL;DR

This paper explores weak invariants in quantum thermodynamics, focusing on time-dependent equilibrium states and isoenergetic processes described by Lindblad equations, with applications to quantum harmonic oscillators.

Contribution

It introduces a method to determine corrections to weak invariants in quantum master equations, analogous to classical Chapman-Enskog expansion, and applies it to finite-time quantum thermodynamics.

Findings

Derived correction method for weak invariants in Lindblad dynamics

Analyzed power output and work in isoenergetic processes

Applied theory to a time-dependent quantum harmonic oscillator

Abstract

The concept of weak invariants is examined in the thermodynamic context. Discussions are made about the temporally-local equilibrium states, corrections to them, and isoenergetic processes based on the quantum master equations of the Lindblad type that admit time-dependent Hamiltonians as weak invariants. The method for determining the correction presented here may be thought of as a quantum-mechanical analog of the Chapman-Enskog expansion in nonequilibrium classical statistical mechanics. Then, the theory is applied to the time-dependent harmonic oscillator as a simple example, and the power output and the work along an isoenergetic process are evaluated within the framework of finite-time quantum thermodynamics.