Ensemble dependence of information-theoretic contributions to the entropy production
arXiv:2301.13061 · doi:10.1103/PhysRevE.107.L052102
Abstract
The entropy production of an open system coupled to a reservoir initialized in a canonical state can be expressed as a sum of two microscopic information-theoretic contributions: the system-bath mutual information and the relative entropy measuring the displacement of the environment from equilibrium. We investigate whether this result can be generalized to situations where the reservoir is initialized in a microcanonical or in a certain pure state (e.g., an eigenstate of a nonintegrable system), such that the reduced dynamics and thermodynamics of the system are the same as for the thermal bath. We show that while in such a case the entropy production can still be expressed as a sum of the mutual information between the system and the bath and a properly redefined displacement term, the relative weight of those contributions depends on the initial state of the reservoir. In other words, different statistical ensembles for the environment predicting the same reduced dynamics for the system give rise to the same total entropy production but to different information-theoretic contributions to the entropy production.
arXiv comment6 pages, 3 figures, with Supplemental Material
References in corpus (41)
- Chaos and Quantum Thermalization
- Nonequilibrium dynamics of closed interacting quantum systems
- From Quantum Chaos and Eigenstate Thermalization to Statistical Mechanics and Thermodynamics
- Nonequilibrium fluctuations, fluctuation theorems, and counting statistics in quantum systems
- Colloquium. Quantum Fluctuation Relations: Foundations and Applications
- Quantum many-body systems out of equilibrium
- Calculation of reduced density matrices from correlation functions
- The foundations of statistical mechanics from entanglement: Individual states vs. averages
- Equilibration, thermalisation, and the emergence of statistical mechanics in closed quantum systems
- Fundamental limitations for quantum and nano thermodynamics
- The second laws of quantum thermodynamics
- Canonical Typicality
- The Resource Theory of Quantum States Out of Thermal Equilibrium
- Eigenstate Thermalization Hypothesis
- Thermalization and prethermalization in isolated quantum systems: a theoretical overview
- Entropy production as correlation between system and reservoir
- From Quantum Dynamics to the Canonical Distribution: General Picture and a Rigorous Example
- Irreversible entropy production, from quantum to classical
- Canonical Thermal Pure Quantum State
- Fluctuation theorem for currents in open quantum systems
- Equivalence and nonequivalence of ensembles: Thermodynamic, macrostate, and measure levels
- First and Second Law of Quantum Thermodynamics: A Consistent Derivation Based on a Microscopic Definition of Entropy
- Strong Coupling Thermodynamics of Open Quantum Systems
- Non-Markovianity and negative entropy production rates
- Fluctuation Theorem for Many-Body Pure Quantum States
- Realizing a Kondo-correlated state with ultracold atoms
- Entropy Production in Open Systems: The Predominant Role of Intra-Environment Correlations
- Spin relaxation in a complex environment
- Quantum systems correlated with a finite bath: nonequilibrium dynamics and thermodynamics
- Clausius Inequality for Finite Baths Reveals Universal Efficiency Improvements
- Selected applications of typicality to real-time dynamics of quantum many-body systems
- Fluctuation, Dissipation and the Arrow of Time
- Quantum master equation for the microcanonical ensemble
- From Linear to Nonlinear Responses of Thermal Pure Quantum States
- Detecting Kondo Entanglement by Electron Conductance
- Universal Thermal Entanglement of Multichannel Kondo Effects
- On the connection between microscopic description and memory effects in open quantum system dynamics
- Thermalization of locally perturbed many-body quantum systems
- Eigenstate Fluctuation Theorem in the Short and Long Time Regimes
- Thermalisation by a boson bath in a pure state
- Integral Fluctuation Theorem for Microcanonical and Pure States
Cited by in corpus (5)
- Comparative Microscopic Study of Entropies and their Production
- Microscopic contributions to the entropy production at all times: From nonequilibrium steady states to global thermalization
- System-bath entanglement of noninteracting fermionic impurities: Equilibrium, transient, and steady-state regimes
- Entropy Production from Maximum Entropy Principle: a Unifying Approach
- Typical Positivity of Nonequilibrium Entropy Production for Pure States