Quantum Dynamics in Classical Time Evolution of Correlation Functions

TL;DR

This paper explores how classical equations of motion govern the time evolution of correlation functions, revealing that many features of quantum dynamics are mirrored in classical systems, with implications for understanding equilibrium and conserved quantities.

Contribution

It demonstrates that classical correlation functions exhibit quantum-like dynamical features and identifies conditions under which equilibrium is or isn't achieved.

Findings

Fixed points of classical correlation evolution can be unstable due to conserved quantities.

Equilibrium is attainable only for certain averaged quantities or subsystems.

Classical dynamics of correlation functions share many features with quantum mechanics.

Abstract

The time-dependence of correlation functions under the influence of classical equations of motion is described by an exact evolution equation. For conservative systems thermodynamic equilibrium is a fixed point of these equations. We show that this fixed point is not universally stable, since infinitely many conserved correlation functions obstruct the approach to equilibrium. Equilibrium can therefore be reached at most for suitably averaged quantities or for subsystems, similar to quantum statistics. The classical time evolution of correlation functions shows many dynamical features of quantum mechanics.