Microscopic Reversibility and Macroscopic Irreversibility: From a viewpoint of Algorithmic Randomness
arXiv:1905.05017 · doi:10.1007/s10955-019-02387-0
Abstract
Emergence of deterministic and irreversible macroscopic behavior from deterministic and reversible microscopic dynamics is understood as a result of the law of large numbers. In this paper, we prove on the basis of the theory of algorithmic randomness that Martin-Löf random initial microstates satisfy an irreversible macroscopic law in the Kac infinite chain model. We find that the time-reversed state of a random state is not random as well as violates the macroscopic law.
arXiv comment21 pages
References in corpus (13)
- Thermalization and its mechanism for generic isolated quantum systems
- The foundations of statistical mechanics from entanglement: Individual states vs. averages
- Canonical Typicality
- Typicality for Generalized Microcanonical Ensembles
- Fluctuation Theorem for Many-Body Pure Quantum States
- Two refreshing views of Fluctuation Theorems through Kinematics Elements and Exponential Martingale
- Typicality of thermal equilibrium and thermalization in isolated macroscopic quantum systems
- Quantum Kolmogorov Complexity Based on Classical Descriptions
- Quantum Algorithmic Entropy
- Work Extraction from a Single Energy Eigenstate
- Thermodynamic Irreversibility from high-dimensional Hamiltonian Chaos
- Macroscopic diffusion from a Hamilton-like dynamics
- Fick's law in a random lattice Lorentz gas