Relations between Dissipated Work and Rényi Divergences

Abstract

In this paper, we establish a general relation which directly links the dissipated work done on a system driven arbitrarily far from equilibrium, a fundamental quantity in thermodynamics, and the Rényi divergences, a fundamental concept in information theory. Specifically, we find that the generating function of the dissipated work under an arbitrary time-dependent driving process is related to the Rényi divergences between a non-equilibrium state in the driven process and a non-equilibrium state in its time reversed process. This relation is a consequence of time reversal symmetry in driven process and is universally applicable to both finite classical system and finite quantum system, arbitrarily far from equilibrium.

5 pages and 2 figures

References in corpus (12)

• Fluctuation theorems: Work is not an observable
• Description of quantum coherence in thermodynamic processes requires constraints beyond free energy
• Dissipation: The phase-space perspective
• Quantum coherence, time-translation symmetry and thermodynamics
• Experimental Test of Quantum Jarzynski Equality with a Trapped Ion System
• 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
• Experimental Free Energy Surface Reconstruction From Single-Molecule Force Spectroscopy Using Jarzynski's Equality
• Irreversibility and the arrow of time in a quenched quantum system
• Quantum work relations and response theory
• The second law of quantum thermodynamics as an equality

Cited by in corpus (17)

• The Wigner Entropy Production Rate
• Quantum work statistics close to equilibrium
• Quantum coherence and criticality in irreversible work
• Quantum work statistics and resource theories: bridging the gap through Renyi divergences
• Measurement-based cooling of a nonlinear mechanical resonator
• Maxwell's Demon walks into Wall Street: Stochastic Thermodynamics meets Expected Utility Theory
• Contributions from populations and coherences in non-equilibrium entropy production
• Quantum Work Relations and Response Theory in $\mathcal{P}\mathcal{T}$-Symmetric Quantum Systems
• Maximum one-shot dissipated work from Renyi divergences
• Links between Dissipation and Rényi Divergences in $\mathcal{P}\mathcal{T}$-Symmetric Quantum Mechanics
• Complexity-constrained quantum thermodynamics
• Relations between Heat Exchange and Rényi Divergences
• Relating relative Rényi entropies and Wigner-Yanase-Dyson skew information to generalized multiple quantum coherences
• Dissipation in the Generalized Gibbs Ensemble
• Irreversible Entropy Production rate in a parametrically driven-dissipative System: The Role of Self-Correlation between Noncommuting Observables
• One-shot information-theoretical approaches to fluctuation theorems
• Fluctuation Relations for Heat Exchange in the Generalized Gibbs Ensemble