Quantum R\'enyi-Jarzynski Equality

Abstract:The Jarzynski equality provides a strict link between nonequilibrium work and equilibrium free energy changes. Its typical quantum formulations, however, rely on measurement protocols that destroy coherence. In this Letter, we use the resource-theoretic approach to derive a non-destructive quantum Jarzynski equality conditioned on the outcomes of an arbitrary bath observable. This yields the Rényi-Jarzynski equality, which quantifies a finite bath's drift from equilibrium under a non-adiabatic drive via the Rényi $k$-divergence. We further demonstrate that the Rényi-Jarzynski equality provides a tunable cost function for quantum optimal control problems where minimizing bath drift is desired, such as state preparation and gate design, enabling the minimization of cross-talk in finite quantum systems. Our toy model exhibits a transition between competing minima for some critical value of $k$, illustrating how the Rényi order tunes sensitivity to different regions of a bath distribution. Strikingly, when drive parameters vary across bath energy levels, minimizing bath drift requires generating system-bath entanglement.

Statistical Mechanics (cond-mat.stat-mech); Chemical Physics (physics.chem-ph); Quantum Physics (quant-ph)

arXiv:2608.19320 [cond-mat.stat-mech]

(or arXiv:2608.19320v1 [cond-mat.stat-mech] for this version)

https://doi.org/10.48550/arXiv.2608.19320 Focus to learn more arXiv-issued DOI via DataCite (pending registration)

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