Irreversibility of Time for Quasi-Isolated Systems

TL;DR

This paper demonstrates that quasi-isolated systems exhibit irreversible evolution characterized by phase-space volume expansion and trajectory divergence, providing a physical explanation for the irreversibility of time.

Contribution

It introduces the concept of local expansion exponents to describe the irreversible behavior of quasi-isolated systems under small perturbations.

Findings

Phase-space volume expands asymptotically at an increasing rate.

Dynamical trajectories diverge with acceleration.

Irreversible evolution explains the arrow of time.

Abstract

A physical system is called quasi-isolated if it subject to small random uncontrollable perturbations. Such a system is, in general, stochastically unstable. Moreover, its phase-space volume at asymptotically large time expands. This can be described by considering the local expansion exponent. Several examples illustrate that the stability indices and expansion exponents of quasi-isolated systems are not only asymptotically positive but are asymptotically increasing. This means that the divergence of dynamical trajectories and the expansion of phase volume at large time occurs with acceleration. Such a strongly irreversible evolution of quasi-isolated systems explains the irreversibility of time.