Thermodynamical path integral and emergent symmetry
arXiv:1812.06375 · doi:10.1103/PhysRevE.99.022109
Abstract
We investigate a thermally isolated quantum many-body system with an external control represented by a step protocol of a parameter. The propagator at each step of the parameter change is described by thermodynamic quantities under some assumptions. For the time evolution of such systems, we formulate a path integral over the trajectories in the thermodynamic state space. In particular, for quasi-static operations, we derive an effective action of the thermodynamic entropy and its canonically conjugate variable. Then, the symmetry for the uniform translation of the conjugate variable emerges in the path integral. This leads to the entropy as a Noether invariant in quantum mechanics.
arXiv comment13 pages. This provides a new formulation for the result discussed in arXiv:1611.07268 which has been withdrawn
References in corpus (36)
- Thermalization and its mechanism for generic isolated quantum systems
- Nonequilibrium dynamics of closed interacting quantum systems
- Black Hole Entropy is Noether Charge
- Nonequilibrium fluctuations, fluctuation theorems, and counting statistics in quantum systems
- Colloquium. Quantum Fluctuation Relations: Foundations and Applications
- Quantum many-body systems out of equilibrium
- Measuring entanglement entropy through the interference of quantum many-body twins
- The foundations of statistical mechanics from entanglement: Individual states vs. averages
- Probing the relaxation towards equilibrium in an isolated strongly correlated 1D Bose gas
- Relaxation and Pre-thermalization in an Isolated Quantum System
- Fundamental limitations for quantum and nano thermodynamics
- The second laws of quantum thermodynamics
- Canonical Typicality
- Quantum mechanical evolution towards thermal equilibrium
- Foundation of Statistical Mechanics under experimentally realistic conditions
- Action functionals for relativistic perfect fluids
- From Quantum Dynamics to the Canonical Distribution: General Picture and a Rigorous Example
- Experimental Test of Quantum Jarzynski Equality with a Trapped Ion System
- Effect of Rare Fluctuations on the Thermalization of Isolated Quantum Systems
- Typicality for Generalized Microcanonical Ensembles
- Von Neumann Algebra Automorphisms and Time-Thermodynamics Relation in General Covariant Quantum Theories
- Canonical Thermal Pure Quantum State
- Thermal Pure Quantum States at Finite Temperature
- Entropy of isolated quantum systems after a quench
- Adiabatic hydrodynamics: The eightfold way to dissipation
- Irreversibility and the arrow of time in a quenched quantum system
- Fluctuation Theorem for Many-Body Pure Quantum States
- Thermal time and the Tolman-Ehrenfest effect: temperature as the "speed of time"
- On the time scales in the approach to equilibrium of macroscopic quantum systems
- Extremely quick thermalization in a macroscopic quantum system for a typical nonequilibrium subspace
- Effective actions for relativistic fluids from holography
- Thermodynamic entropy as a Noether invariant
- The Second Law of Thermodynamics under Unitary Evolution and External Operations
- Death and resurrection of the zeroth principle of thermodynamics
- On the Basis of Quantum Statistical Mechanics
- Variational formulation of ideal fluid flows according to gauge principle
Cited by in corpus (14)
- Why Noether's Theorem applies to Statistical Mechanics
- Noether-Constrained Correlations in Equilibrium Liquids
- Why neural functionals suit statistical mechanics
- Hyper-density functional theory of soft matter
- Variance of fluctuations from Noether invariance
- Gauge Invariance of Equilibrium Statistical Mechanics
- Hyperforce balance via thermal Noether invariance of any observable
- Noether invariance theory for the equilibrium force structure of soft matter
- Thermodynamic entropy as a Noether invariant in a Langevin equation
- Why gauge invariance applies to statistical mechanics
- Gauge invariance and hyperforce correlation theory for equilibrium fluid mixtures
- Self-Gravity and Bekenstein-Hawking Entropy
- First part of Clausius heat theorem in terms of Noether's theorem
- Entropy as Noether charge for quasistatic gradient flow