Maximum one-shot dissipated work from Renyi divergences

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.

8 pages. Close to published version

References in corpus (19)

• Dissipation: The phase-space perspective
• Experimental Test of Quantum Jarzynski Equality with a Trapped Ion System
• The Statistics of the Work Done on a Quantum Critical System by Quenching a Control Parameter
• Rare events and the convergence of exponentially averaged work values
• Generalized Clausius inequality for nonequilibrium quantum processes
• Test of Jarzynski and Crooks fluctuation relations in an electronic system
• Fully quantum fluctuation theorems
• The second law of quantum thermodynamics as an equality
• Quantum Quench Dynamics in the Transverse Field Ising Model at Non-zero Temperatures
• On the work distribution for the adiabatic compression of a dilute classical gas
• The "footprints'' of irreversibility
• Smoothed generalized free energies for thermodynamics
• Jarzynski Equality for Driven Quantum Field Theories
• Number of trials required to estimate a free-energy difference, using fluctuation relations
• Quantum to classical transition in the work distribution for chaotic systems
• Work distributions for random sudden quantum quenches
• Relations between Dissipated Work and Rényi Divergences
• Fluctuations in Single-Shot $\epsilon$-Deterministic Work Extraction
• Entropic equality for worst-case work at any protocol speed

Cited by in corpus (8)

• Initial-State Dependence of Thermodynamic Dissipation for any Quantum Process
• Quantum work statistics and resource theories: bridging the gap through Renyi divergences
• Maxwell's Demon walks into Wall Street: Stochastic Thermodynamics meets Expected Utility Theory
• Fluctuation-dissipation relations for thermodynamic distillation processes
• Lower bound for entropy production rate in stochastic systems far from equilibrium
• Complexity-constrained quantum thermodynamics
• Toward the nonequilibrium thermodynamic analog of complexity and the Jarzynski identity
• One-shot information-theoretical approaches to fluctuation theorems