Broken versus Non-Broken Time Reversal Symmetry: Irreversibility and Response

Sara Dal Cengio,Lamberto Rondoni

doi:10.3390/sym8080073

Abstract

We review some approaches to macroscopic irreversibility from reversible microscopic dynamics, introducing the contribution of time dependent perturbations within the framework of recent developments in non-equilibrium statistical physics. We show that situations commonly assumed to violate the time reversal symmetry (presence of magnetic fields, rotating reference frames, and some time dependent perturbations) in reality do not violate this symmetry, and can be treated with standard theories and within standard experimental protocols.

Highlights

Temporal irreversibility is one of the classic questions of physics, because it deals with the most common experience of our daily life, but it looks at odds with our understanding of the properties of the microscopic constituents of matter
If we express relaxation towards a steady state in terms of the behaviour of observables of a system, which is the way we establish equilibrium, Equation (70) states that: under weak t-mixing, single systems relax in a typical fashion, where typical is intended in the sense of counting even for dissipative dyamics. In this contribution we have outlined a physical interpretation of the problem of macroscopic irreversibility, the temporal symmetry breaking of our daily life space and time scales, for relaxation of time reversal invariant (TRI) dissipative systems, such as those of nonequilibrium molecular dynamics (NEMD)
In the case of conservative dynamics, the standard approach is represented by Boltzmann’s argument. This argument rests on the notion of typicality, which implies that a system starting in a non-equilibrium state with dynamics exploring the phase space without constraints irreversibly enters its proper equilibrium state

Summary

Introduction

Temporal irreversibility is one of the classic questions of physics, because it deals with the most common experience of our daily life, but it looks at odds with our understanding of the properties of the microscopic constituents of matter. For a rarefied gas of particles, the joint probability distribution of positions and momenta can be factorized in the product of single-particle distributions, which means that correlations between interacting particles must decay after some short time due to collisions This merely statistical idea of loss of memory, being alien to classical mechanics, was hardly acceptable for most of the scientists of that period. This question leads to the very core of the dissertation: for a macroscopic system close to equilibrium, the dynamics captured by the Boltzmann equation, which is relaxation towards states of higher and higher disorder, are the only physically significant ones This irreversible trend toward homogeneity does not derive directly from classical mechanics laws, since they are perfectly reversible.

Standard Picture for Irreversible Relaxation to Equilibrium

Time Reversible Dissipative Dynamics

The Dissipation Function

Time-Dependent Perturbations

Fluctuation Relations

Conclusions