# Transition to thermal equilibrium in a deformed crystal

## TL;DR

This paper analyzes how an infinite particle chain transitions between equilibrium states with different stiffnesses, revealing oscillatory and non-monotonic temperature evolution through analytical and numerical methods.

## Contribution

It provides analytical expressions for temperature evolution during a sudden parameter change in a particle chain, highlighting unexpected oscillatory behavior.

## Key findings

- Transition process is oscillatory and non-monotonic.
- Analytical expressions for temperature as a function of time.
- Numerical simulations support analytical results.

## Abstract

An adiabatic transition between two equilibrium states corresponding to different stiffnesses in an infinite chain of particles is studied. Initially, the chain particles have random displacements and random velocities corresponding to a uniform initial temperature. An instant change of parameters of chain initiates a transient process. Analytical expressions for the chain temperature as a function of time are obtained from the statistical analysis of the dynamics equations. It is shown that the transition process is oscillatory and it converges non-monotonically to a new equilibrium state. Such behavior is usually unexpected for thermal processes. The analytical results are supplemented by numerical simulations.