# Steady state of isolated systems versus microcanonical ensemble in cell model of particle creation and annihilation

## TL;DR

This paper introduces a simple cell model for particle creation and annihilation in an isolated system, analyzing its steady state distribution and comparing it with microcanonical ensemble predictions, highlighting conditions for agreement.

## Contribution

The paper formulates a cell model for particle creation and annihilation, and compares its steady state with microcanonical ensemble predictions, revealing conditions for their agreement.

## Key findings

- Steady state distribution approaches time-independence over time.
- Microcanonical ensemble predictions differ unless creation and annihilation probabilities are equal.
- Equality of probabilities leads to detailed balance in the steady state.

## Abstract

A simple model of particle creation and annihilation in an isolated assembly of particles with conserved energy and fixed volume, the Cell Model, is formulated. With increasing time, particle number distribution, obtained by averaging over many systems, approaches a time-independent, steady state distribution. Dependence of the steady state distribution on creation and annihilation conditional reaction probabilities is studied. The results obtained for the steady state are compared with predictions of statistical mechanics within the microcanonical ensemble. In general, the predictions of both models are different. They agree only if the creation and annihilation conditional probabilities are equal. This condition also results in the detailed balance in the steady state.