Quantum work statistics and resource theories: Bridging the gap through Rényi divergences

Abstract

The work performed on or extracted from a non-autonomous quantum system described by means of a twopoint projective-measurement approach takes the form of a stochastic variable. We show that the cumulant generating function of work can be recast in the form of quantum Rényi-α divergences, and by exploiting convexity of this cumulant generating function, derive a single-parameter family of bounds for the first moment of work. Higher order moments of work can also be obtained from this result. In this way, we establish a link between quantum work statistics in stochastic approaches on the one hand and resource theories for quantum thermodynamics on the other hand, a theory in which Rényi-α divergences take a central role. To explore this connection further, we consider an extended framework involving a control switch and an auxiliary battery, which is instrumental to reconstruct the work statistics of the system. We compare and discuss our bounds on the work distribution to findings on deterministic work studied in resource theoretic settings.

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