Non-equilibrium spin-boson model: counting statistics and the heat exchange fluctuation theorem

TL;DR

This paper investigates quantum thermal transport in the non-equilibrium spin-boson model, deriving fluctuation theorems and heat current expressions, especially under strong system-bath coupling and non-Markovian dynamics.

Contribution

It provides the first derivation of the steady-state heat exchange fluctuation theorem for the non-equilibrium spin-boson model, including non-Markovian effects.

Findings

Validation of the steady-state heat exchange fluctuation theorem in quantum systems.

Analytic expression for heat current in the spin-boson model.

Identification of a weaker symmetry relation in non-Markovian regimes.

Abstract

We focus on the non-equilibrium two-bath spin-boson model, a toy model for examining quantum thermal transport in many-body open systems. Describing the dynamics within the NIBA equations, applicable, e.g., in the strong system-bath coupling limit and/or at high temperatures, we derive expressions for the cumulant generating function in both the markovian and non-markovian limits by energy-resolving the quantum master equation of the subsystem. For a markovian bath, we readily demonstrate the validity of a steady-state heat exchange fluctuation theorem. In the non-markovian limit a "weaker" symmetry relation generally holds, a general outcome of microreversibility. We discuss the reduction of this symmetry relation to the universal steady-state fluctuation theorem. Using the cumulant generating function, an analytic expression for the heat current is obtained. Our results establish the validity of the steady-state heat exchange fluctuation theorem in quantum systems with strong system-bath interactions. From the practical point of view, this study provides tools for exploring transport characteristics of the two-bath spin-boson model, a prototype for a nonlinear thermal conductor.