Classicality, Markovianity and local detailed balance from pure state dynamics
arXiv:2209.07977 · doi:10.1103/PhysRevA.108.012225
Abstract
When describing the effective dynamics of an observable in a many-body system, the repeated randomness assumption, which states that the system returns in a short time to a maximum entropy state, is a crucial hypothesis to guarantee that the effective dynamics is classical, Markovian and obeys local detailed balance. While the latter behaviour is frequently observed in naturally occurring processes, the repeated randomness assumption is in blatant contradiction to the microscopic reversibility of the system. Here, we show that the use of the repeated randomness assumption can be justified in the description of the effective dynamics of an observable that is both slow and coarse, two properties we will define rigorously. Then, our derivation will invoke essentially only the eigenstate thermalization hypothesis and typicality arguments. While the assumption of a slow observable is subtle, as it provides only a necessary but not sufficient condition, it also offers a unifying perspective applicable to, e.g., open systems as well as collective observables of many-body systems. All our ideas are numerically verified by studying density waves in spin chains.
Final version
References in corpus (27)
- Thermalization and its mechanism for generic isolated quantum systems
- Quantum Non-Markovianity: Characterization, Quantification and Detection
- Quantum Darwinism
- Foundation of Statistical Mechanics under experimentally realistic conditions
- Quantum Decoherence
- Proof of the Ergodic Theorem and the H-Theorem in Quantum Mechanics
- Off-diagonal matrix elements of local operators in many-body quantum systems
- Quantum stochastic processes and quantum non-Markovian phenomena
- Generalization of von Neumann's Approach to Thermalization
- Low-frequency behavior of off-diagonal matrix elements in the integrable XXZ chain and in a locally perturbed quantum-chaotic XXZ chain
- Timescales of quantum equilibration, dissipation and fluctuation in nuclear collisions
- Eigenstate thermalization hypothesis and its deviations from random-matrix theory beyond the thermalization time
- Out-of-time-order correlations and the fine structure of eigenstate thermalisation
- Quantum Theory of the Classical: Einselection, Envariance, Quantum Darwinism and Extantons
- Speed Limits for Macroscopic Transitions
- Non-Abelian eigenstate thermalization hypothesis
- Typicality of Prethermalization
- Critical review of prevailing explanations for the emergence of classicality in cosmology
- Finite quantum environments as thermostats: an analysis based on the Hilbert space average method
- Typical Relaxation of Isolated Many-Body Systems Which Do Not Thermalize
- Classicality with(out) decoherence: Concepts, relation to Markovianity, and a random matrix theory approach
- Relaxation of Multitime Statistics in Quantum Systems
- Typical relaxation of perturbed quantum many-body systems
- Typicality of nonequilibrium (quasi-)steady currents
- Equilibration of Multitime Quantum Processes in Finite Time Intervals
- Classical Lieb-Robinson Bound for Estimating Equilibration Timescales of Isolated Quantum Systems
- Decoherence Entails Exponential Forgetting in Systems Complying with the Eigenstate Thermalization Hypothesis
Cited by in corpus (21)
- Noncommuting conserved charges in quantum thermodynamics and beyond
- First Principles Numerical Demonstration of Emergent Decoherent Histories
- Characterising the Hierarchy of Multi-time Quantum Processes with Classical Memory
- Continuity bounds on observational entropy and measured relative entropies
- Quantum master equation from the eigenstate thermalization hypothesis
- On the generic increase of observational entropy in isolated systems
- Objectivity of classical quantum stochastic processes
- Canonical Typicality For Other Ensembles Than Micro-Canonical
- Comparative Microscopic Study of Entropies and their Production
- Microscopic contributions to the entropy production at all times: From nonequilibrium steady states to global thermalization
- Long-time equilibration can determine transient thermality
- Typical Macroscopic Long-Time Behavior for Random Hamiltonians
- Macroscopic Thermalization for Highly Degenerate Hamiltonians After Slight Perturbation
- Decoherence of Histories: Chaotic Versus Integrable Systems
- Entropic partial orderings of quantum measurements
- Evidence for simple "arrow of time functions" in closed chaotic quantum systems
- Canonical typicality under general quantum channels
- Purely quantum memory in closed systems observed via imperfect measurements
- Typical Positivity of Nonequilibrium Entropy Production for Pure States
- Toy Model Challenging Prevailing Definitions of Classicality
- Diagnosing chaos with projected ensembles of process tensors