Statistical Mechanics of Discrete Multicomponent Fragmentation

TL;DR

This paper applies statistical mechanics principles to model and analyze the distributions of fragments resulting from multicomponent fragmentation events, providing analytical formulas and simulation validation.

Contribution

It introduces a novel statistical mechanics framework for multicomponent fragmentation, deriving closed-form expressions for distributions and biasing mechanisms.

Findings

Derived the partition function and mean distribution analytically.

Validated theoretical results with Monte Carlo simulations.

Demonstrated component segregation and mixing behaviors.

Abstract

We formulate the statistics of the discrete multicomponent fragmentation event using a methodology borrowed from statistical mechanics. We generate the ensemble of all feasible distributions that can be formed when a single integer multicomponent mass is broken into fixed number of fragments and calculate the combinatorial multiplicity of all distributions in the set. We define random fragmentation by the condition that the probability of distribution be proportional to its multiplicity and obtain the partition function and the mean distribution in closed form. We then introduce a functional that biases the probability of distribution to produce in a systematic manner fragment distributions that deviate to any arbitrary degree from the random case. We corroborate the results of the theory by Monte Carlo simulation and demonstrate examples in which components in sieve cuts of the fragment distribution undergo preferential mixing or segregation relative to the parent particle.