Irreversibility from a Reversible Equation

TL;DR

This paper demonstrates that a reversible equation of motion, with inhomogeneous initial temperature, can produce irreversible diffusive behavior, highlighting the subtlety of irreversibility in thermodynamic systems.

Contribution

It introduces a simple model showing how reversible dynamics can lead to apparent irreversibility through initial conditions with temperature inhomogeneity.

Findings

Reversible equations can produce diffusive, irreversible behavior.

Diffusion occurs both forward and backward in time, maintaining time symmetry.

Initial temperature inhomogeneity is key to the observed irreversibility.

Abstract

After a discussion on the state of local equilibrium with temperature inhomogeneity, comparing mixture state reprsentation in statistical mechanics and pure state representation in thermo field dynamics, a simple model is solved to show that a reversible equation of motion with the initial condition having inhomogeneous temperature can lead to irreversible, viz. diffusive, behaviour. Yet, the solution is time symmetric exhibiting diffusion both towards future and past.