Extremum complexity in the monodimensional ideal gas: the piecewise uniform density distribution approximation

TL;DR

This paper proposes that extremum complexity distributions in high-dimensional systems can be approximated as piecewise uniform or exponential distributions, simplifying the analysis of out-of-equilibrium states, demonstrated through a 1D ideal gas model.

Contribution

It introduces a novel interpretation of extremum complexity distributions as piecewise uniform or exponential functions for high-dimensional dynamical systems.

Findings

Numerical simulations show the energy distribution of a 1D ideal gas forms two non-overlapping Gaussians.

The approach simplifies the description of systems far from equilibrium.

Experimental observations in granular systems are consistent with the proposed distributions.

Abstract

In this work, it is suggested that the extremum complexity distribution of a high dimensional dynamical system can be interpreted as a piecewise uniform distribution in the phase space of its accessible states. When these distributions are expressed as one--particle distribution functions, this leads to piecewise exponential functions. It seems plausible to use these distributions in some systems out of equilibrium, thus greatly simplifying their description. In particular, here we study an isolated ideal monodimensional gas far from equilibrium that presents an energy distribution formed by two non--overlapping Gaussian distribution functions. This is demonstrated by numerical simulations. Also, some previous laboratory experiments with granular systems seem to display this kind of distributions.