Two-Time Measurement of Entropy Transfer in Markovian Quantum Dynamics

TL;DR

This paper develops a protocol for measuring entropy transfer in Markovian quantum systems, linking it to entropy production and showing measurement outcomes follow a Markov process governed by Lindblad dynamics.

Contribution

It introduces a two-time measurement protocol for entropic observables in open quantum systems and connects measurement outcomes to Lindblad-driven Markov processes.

Findings

Expected entropy variations relate to known entropy production formulas.

Measurement outcomes follow a continuous-time Markov process.

The protocol applies under detailed balance conditions.

Abstract

We consider a protocol for the two-time measurement of entropic observables in quantum open systems driven out of thermal equilibrium by coupling to several heat baths. We concentrate on the Markovian approximation of the time-evolution and relate the expected value of the so defined entropy variations with the well-known expression of entropy production due to Lebowitz and Spohn. We do so under the detailed balance condition and, as a byproduct, we show that the probabilities of outcomes of two-time measurements are given by a continuous time Markov process determined by the Lindblad generator of the Markovian quantum dynamics.