Comparative Microscopic Study of Entropies and their Production
arXiv:2403.09403 · doi:10.21468/SciPostPhys.17.5.143
Abstract
We study the time evolution of eleven microscopic entropy definitions (of Boltzmann-surface, Gibbs-volume, canonical, coarse-grained-observational, entanglement and diagonal type) and three microscopic temperature definitions (based on Boltzmann, Gibbs or canonical entropy). This is done for the archetypal nonequilibrium setup of two systems exchanging energy, modeled here with random matrix theory, based on numerical integration of the Schroedinger equation. We consider three types of pure initial states (local energy eigenstates, decorrelated and entangled microcanonical states) and three classes of systems: (A) two normal systems, (B) a normal and a negative temperature system and (C) a normal and a negative heat capacity system. We find: (1) All types of initial states give rise to the same macroscopic dynamics. (2) Entanglement and diagonal entropy sensitively depend on the microstate, in contrast to all other entropies. (3) For class B and C, Gibbs-volume entropies can violate the second law and the associated temperature becomes meaningless. (4) For class C, Boltzmann-surface entropies can violate the second law and the associated temperature becomes meaningless. (5) Canonical entropy has a tendency to remain almost constant. (6) For a Haar random initial state, entanglement or diagonal entropy behave similar or identical to coarse-grained-observational entropy.
arXiv commentSlight changes compared to v1. 15.5 pages with big figures plus references. Comments and discussion still very welcome!
References in corpus (58)
- Many-Body Physics with Ultracold Gases
- Chaos and Quantum Thermalization
- Area laws for the entanglement entropy - a review
- Random-Matrix Theory of Quantum Transport
- From Quantum Chaos and Eigenstate Thermalization to Statistical Mechanics and Thermodynamics
- Random Matrix Theories in Quantum Physics: Common Concepts
- The large deviation approach to statistical mechanics
- The holographic principle
- Evolution of Entanglement Entropy in One-Dimensional Systems
- Probing the relaxation towards equilibrium in an isolated strongly correlated 1D Bose gas
- Statistical mechanics and dynamics of solvable models with long-range interactions
- Thermodynamical Aspects of Gravity: New insights
- Eigenstate Thermalization Hypothesis
- The approach to thermal equilibrium in quantized chaotic systems
- Entanglement and thermodynamics after a quantum quench in integrable systems
- Alternatives to Eigenstate Thermalization
- A thermoelectric heat engine with ultracold atoms
- Long-range interacting quantum systems
- Negative Absolute Temperature for Motional Degrees of Freedom
- Proof of the Ergodic Theorem and the H-Theorem in Quantum Mechanics
- Microscopic diagonal entropy and its connection to basic thermodynamic relations
- Temperature in and out of equilibrium: a review of concepts, tools and attempts
- Dynamical typicality of quantum expectation values
- Inconsistent thermostatistics and negative absolute temperatures
- Entropy of isolated quantum systems after a quench
- First and Second Law of Quantum Thermodynamics: A Consistent Derivation Based on a Microscopic Definition of Entropy
- Gibbs, Boltzmann, and negative temperatures
- Normal Typicality and von Neumann's Quantum Ergodic Theorem
- Generalization of von Neumann's Approach to Thermalization
- Quantum coarse-grained entropy and thermodynamics
- Entropy Production in Open Systems: The Predominant Role of Intra-Environment Correlations
- Quantum coarse-grained entropy and thermalization in closed systems
- Direct measurement of nonequilibrium system entropy is consistent with Gibbs-Shannon form
- Construction of microcanonical entropy on thermodynamic pillars
- Statistical Mechanics of Systems with Negative Temperature
- The Boltzmann Entropy for Dense Fluids Not in Local Equilibrium
- Dynamical typicality of isolated many-body quantum systems
- A brief introduction to observational entropy
- Clausius Inequality for Finite Baths Reveals Universal Efficiency Improvements
- Occurrence of exponential relaxation in closed quantum systems
- Classical dynamical coarse-grained entropy and comparison with the quantum version
- Classicality, Markovianity and local detailed balance from pure state dynamics
- Why are macroscopic experiments reproducible? Imitating the behavior of an ensemble by single pure states
- Typical and extreme entropies of long-lived isolated quantum systems
- Entropy growth during free expansion of an ideal gas
- The thermodynamic entropy of a macroscopic quantum system is a continuous function of energy
- Numerically "exact" simulations of entropy production in the fully quantum regime: Boltzmann entropy versus von Neumann entropy
- First Principles Numerical Demonstration of Emergent Decoherent Histories
- Boltzmann entropy of a freely expanding quantum ideal gas
- Chaos due to symmetry-breaking in deformed Poisson ensemble
- Refining Deutsch's approach to thermalization
- Typicality of nonequilibrium (quasi-)steady currents
- Time Evolution of Typical Pure States from a Macroscopic Hilbert Subspace
- Entropy and the second law for driven, or quenched, thermally isolated systems
- Observational entropic study of Anderson localization
- Quantum and classical contributions to entropy production in fermionic and bosonic Gaussian systems
- Ensemble dependence of information-theoretic contributions to the entropy production
- Microscopic contributions to the entropy production at all times: From nonequilibrium steady states to global thermalization