Dephasing and dissipation in qubit thermodynamics

TL;DR

This paper investigates how dephasing and dissipation affect the validity of fluctuation relations in qubit thermodynamics, using the quantum jump approach to analyze individual inelastic processes and their impact on non-equilibrium statistical mechanics.

Contribution

It demonstrates that fluctuation relations remain valid under weak dissipation when considering full quantum trajectories, contrasting with standard measurement protocols that show deviations.

Findings

Fluctuation relations hold in the weak dissipation limit with quantum jump analysis.

Standard two-measurement protocols deviate from fluctuation relations under dephasing.

The relation between average exponential work and relaxation/dephasing rates is established.

Abstract

We analyze the stochastic evolution and dephasing of a qubit within the quantum jump (QJ) approach. It allows one to treat individual realizations of inelastic processes, and in this way it provides solutions, for instance, to problems in quantum thermodynamics and distributions in statistical mechanics. As a solvable example, we study a qubit in the weak dissipation limit, and demonstrate that dephasing and relaxation render the Jarzynski and Crooks fluctuation relations (FRs) of non-equilibrium thermodynamics intact. On the contrary, the standard two-measurement protocol, taking into account only the fluctuations of the internal energy $U$, leads to deviations in FRs under the same conditions. We relate the average $\langle e^{-\beta U} \rangle $ (where $\beta$ is the inverse temperature) with the qubit's relaxation and dephasing rates, and discuss this relationship for different mechanisms of decoherence.