Strong coupling non-Markovian quantum thermodynamics of a finite-bath system

TL;DR

This paper investigates the quantum thermodynamics of a strongly coupled, non-Markovian spin system, deriving exact dynamics and thermodynamic quantities, and explores the implications for quantum batteries and the Hamiltonian of mean force.

Contribution

It provides an exact solution for a non-Markovian spin bath model and analyzes thermodynamic quantities in the strong coupling regime, including the role of the Hamiltonian of mean force.

Findings

Explicit expression for work in strong coupling

Mismatch between system and bath internal energies

Spin bath can act as a charger for quantum batteries

Abstract

The focus is on understanding the quantum thermodynamics of strongly coupled non-Markovian quantum systems. To this end, a non-trivial, non-Markovian model of a central spin surrounded by a spin bath is taken up, and its exact evolution is derived for arbitrary system-bath couplings. The fundamental quantum thermodynamic quantities, such as system and bath internal energies, work, heat, entropy production, and ergotropy, are calculated using the dynamics and original system (bath) Hamiltonian. An explicit expression for the work, a mismatch between the system and bath internal energies, is derived. The thermodynamic entropy of the system at thermal equilibrium is studied using the Hamiltonian of mean force in the strong coupling regime. The role of a canonical Hamiltonian in calculating the above thermodynamic quantities, a recently developed technique, is also investigated. Further, an interesting observation relevant to the spin bath acting as a charger is made in a scenario where the central spin is envisaged as a quantum battery.