Maximum one-shot dissipated work from Renyi divergences

TL;DR

This paper introduces a one-shot framework for dissipated work in thermodynamics, linking fluctuation theorems and one-shot statistical mechanics through Renyi divergences, especially the order-infinity divergence.

Contribution

It derives one-shot analogs of fluctuation theorem equations, showing the maximum dissipated work relates to the order-infinity Renyi divergence, unifying two approaches in small-scale thermodynamics.

Findings

Maximum dissipated work is proportional to the order-infinity Renyi divergence.

Derived one-shot analogs of fluctuation theorem equations.

Unified fluctuation theorems and one-shot statistical mechanics.

Abstract

Thermodynamics describes large-scale, slowly evolving systems. Two modern approaches generalize thermodynamics: fluctuation theorems, which concern finite-time nonequilibrium processes, and one-shot statistical mechanics, which concerns small scales and finite numbers of trials. Combining these approaches, we calculate a one-shot analog of the average dissipated work defined in fluctuation contexts: the cost of performing a protocol in finite time instead of quasistatically. The average dissipated work has been shown to be proportional to a relative entropy between phase-space densities, to a relative entropy between quantum states, and to a relative entropy between probability distributions over possible values of work. We derive one-shot analogs of all three equations, demonstrating that the order-infinity Renyi divergence is proportional to the maximum possible dissipated work in each case. These one-shot analogs of fluctuation-theorem results contribute to the unification of these two toolkits for small-scale, nonequilibrium statistical physics.