From Time-symmetric Microscopic Dynamics to Time-asymmetric Macroscopic Behavior: An Overview

Abstract

Time-asymmetric behavior as embodied in the second law of thermodynamics is observed in {\it individual macroscopic} systems. It can be understood as arising naturally from time-symmetric microscopic laws when account is taken of a) the great disparity between microscopic and macroscopic scales, b) a low entropy state of the early universe, and c) the fact that what we observe is the behavior of systems coming from such an initial state--not all possible systems. The explanation of the origin of the second law based on these ingredients goes back to Maxwell, Thomson and particularly Boltzmann. Common alternate explanations, such as those based on the ergodic or mixing properties of probability distributions (ensembles) already present for chaotic dynamical systems having only a few degrees of freedom or on the impossibility of having a truly isolated system, are either unnecessary, misguided or misleading. Specific features of macroscopic evolution, such as the diffusion equation, do however depend on the dynamical instability (deterministic chaos) of trajectories of isolated macroscopic systems. The extensions of these classical notions to the quantum world is in many ways fairly direct. It does however also bring in some new problems. These will be discussed but not resolved.

References in corpus (4)

• The foundations of statistical mechanics from entanglement: Individual states vs. averages
• Canonical Typicality
• On the (Boltzmann) Entropy of Nonequilibrium Systems
• On the Distribution of the Wave Function for Systems in Thermal Equilibrium

Cited by in corpus (17)

• On the Approach to Thermal Equilibrium of Macroscopic Quantum Systems
• Typicality of thermal equilibrium and thermalization in isolated macroscopic quantum systems
• Thermal equilibrium of a macroscopic quantum system in a pure state
• Compatibility of linear-response theory with the Second Law of Thermodynamics and the emergence of negative entropy production rates
• Is the Hypothesis About a Low Entropy Initial State of the Universe Necessary for Explaining the Arrow of Time?
• Time Irreversibility Problem and Functional Formulation of Classical Mechanics
• Entropy growth during free expansion of an ideal gas
• Quantum statistical mechanical derivation of the second law of thermodynamics: a hybrid setting approach
• The definition of the thermodynamic entropy in statistical mechanics
• Critique of the Gibbs volume entropy and its implication
• The approach to thermal equilibrium and "thermodynamic normality" --- An observation based on the works by Goldstein, Lebowitz, Mastrodonato, Tumulka, and Zanghi in 2009, and by von Neumann in 1929
• Gravity, Entropy, and Cosmology: In Search of Clarity
• The Fine-Tuning Argument
• How and why does statistical mechanics work
• Derivation of the Boltzmann equation and entropy production in functional mechanics
• Hierarchy of space-time structures, Boltzmann equation, and functional mechanics
• Microscopic Origins of Macroscopic Behavior