Numerical calculation of the energy relative fluctuation for a system in contact with a finite heat bath

TL;DR

This paper numerically investigates the energy fluctuation in finite systems coupled to a heat bath, confirming theoretical predictions and suggesting ergodic behavior without poor statistical properties.

Contribution

It introduces a numerical scheme to compute energy fluctuations in finite systems and validates previous theoretical results using simulations of harmonic and quartic oscillators.

Findings

Numerical results agree with theoretical predictions.

Finite systems exhibit ergodic behavior.

Finite systems do not produce poor statistical distributions.

Abstract

We use a scheme of separation of degrees of freedom for a system, in order to produce two systems with finite number of degrees of freedom. Our intent is to measure the energy square relative fluctuation (SRF) of the observable part through the simulation of two simple examples of composed systems, the harmonic oscillator, and the chain of quartic oscillators. We want to test the result found previously by us through the finite heat bath canonical ensemble (cond-mat/0210525), which is an application of Tsallis' statistics. We see that the results found here are in very good agreement with the theoretical predicted value. This suggests that this kind of finite systems is ergodic, and that they do not provide ``bad'' statistics.