Interplay between Standard Quantum Detailed Balance and Thermodynamically Consistent Entropy Production

TL;DR

This paper establishes a precise equivalence between standard quantum detailed balance and thermodynamic entropy production rate vanishing in finite-dimensional quantum Markov semigroups.

Contribution

It provides a characterization linking detailed balance conditions with entropy production, clarifying their interplay in quantum thermodynamics.

Findings

Standard quantum detailed balance implies a special generator representation with zero entropy production.

A generator with a thermodynamically consistent form and zero entropy production satisfies detailed balance.

The results connect physical definitions of entropy production with mathematical properties of quantum Markov semigroups.

Abstract

We demonstrate that, for a quantum Markovian semigroup on a finite-dimensional Hilbert space, if it satisfies the standard quantum detailed balance condition, its generator admits a special representation that yields a vanishing entropy production rate. Conversely, if the generator admits a special representation adhering to the condition of thermodynamic consistency and leading to a vanishing entropy production rate, then the corresponding quantum Markovian semigroup must satisfy the standard quantum detailed balance condition. In this context, we adopt the definition of entropy production rate that is motivated by the physics literature and standard for thermodynamically consistent Lindbladians.