Links between Dissipation and Rényi Divergences in $\mathcal{P}\mathcal{T}$-Symmetric Quantum Mechanics

Abstract

Thermodynamics and information theory have been intimately related since the times of Maxwell and Boltzmann. Recently it was shown that the dissipated work in an arbitrary non-equilibrium process is related to the Rényi divergences between two states along the forward and reversed dynamics. Here we show that the relation between dissipated work and Renyi divergences generalizes to $\mathcal{P}\mathcal{T}$-symmetric quantum mechanics with unbroken $\mathcal{P}\mathcal{T}$ symmetry. In the regime of broken $\mathcal{P}\mathcal{T}$ symmetry, the relation between dissipated work and Renyi divergences does not hold as the norm is not preserved during the dynamics. This finding is illustrated for an experimentally relevant system of two-coupled cavities.

arXiv comment7 pages

References in corpus (38)

• A nonequilibrium equality for free energy differences
• Rényi Divergence and Kullback-Leibler Divergence
• Nonequilibrium fluctuations, fluctuation theorems, and counting statistics in quantum systems
• Colloquium. Quantum Fluctuation Relations: Foundations and Applications
• Verification of the Crooks fluctuation theorem and recovery of RNA folding free energies
• Fluctuation theorems: Work is not an observable
• On quantum Renyi entropies: a new generalization and some properties
• The Nonequilibrium Thermodynamics of Small Systems
• Observation of non-Hermitian degeneracies in a chaotic exciton-polariton billiard
• Dissipation: The phase-space perspective
• Experimental Test of Quantum Jarzynski Equality with a Trapped Ion System
• Experimental reconstruction of work distribution and verification of fluctuation relations at the full quantum level
• Thermodynamics of a Colloidal Particle in a Time-Dependent Non-Harmonic Potential
• Rare events and the convergence of exponentially averaged work values
• Extracting quantum work statistics and fluctuation theorems by single qubit interferometry
• Sandwiched Rényi Divergence Satisfies Data Processing Inequality
• Measuring the characteristic function of the work distribution
• Generalized Clausius inequality for nonequilibrium quantum processes
• Entropy production and the arrow of time
• An experimental test of the Jarzynski equality in a mechanical experiment
• 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
• Observation of Lee-Yang zeros
• Emergent thermodynamics in a quenched quantum many-body system
• Dissipation and lag in irreversible processes
• A Quantum Fluctuation Theorem
• Irreversibility and the arrow of time in a quenched quantum system
• Probing Lee-Yang zeros and coherence sudden death
• Time Dependent $\mathcal{P}\mathcal{T}$-Symmetric Quantum Mechanics
• Trajectory phase transitions, Lee-Yang zeros, and high-order cumulants in full counting statistics
• Non-hermitian quantum thermodynamics
• Experimental Determination of Dynamical Lee-Yang Zeros
• Jarzynski equality in $\mathcal{P}\mathcal{T}$-symmetric quantum mechanics
• Phase transitions in the complex plane of physical parameters
• Universal Critical Behaviors in Non-Hermitian Phase Transitions
• Probing Yang-Lee Edge Singularity by Central Spin Decoherence
• Relations between Dissipated Work and Rényi Divergences
• Thermodynamic holography

Cited by in corpus (6)

• Quantum Geometric Tensor in $\mathcal{P}\mathcal{T}$-Symmetric Quantum Mechanics
• Time-dependent $\mathcal{P}\mathcal{T}$-symmetric quantum mechanics in generic non-Hermitian systems
• Constraining work fluctuations of non-Hermitian dynamics across the exceptional point of a superconducting qubit
• Relations between Heat Exchange and Rényi Divergences
• Dissipation in the Generalized Gibbs Ensemble
• Fluctuation Relations for Heat Exchange in the Generalized Gibbs Ensemble