Maximum one-shot dissipated work from Rényi divergences

Journal article

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 Rényi 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.

Authors: Yunger Halpern, N; Garner, A; Dahlsten, O; Vedral, V

• Publication status: Published
• Peer review status: Peer reviewed
• Publisher: American Physical Society
• Journal: Physical Review E
• Volume: 97
• Issue: 5-1
• Article number: 052135
• Publication date: 2018-05-25
• Acceptance date: 2018-05-25
• DOI: 10.1103/physreve.97.052135
• EISSN: 2470-0053
• ISSN: 2470-0045
• Pmid: 29906852
• Language: English
• Keywords: FFR