# Monte Carlo Simulation on Adiabatic Ensembles and a Genetic Algorithm

## TL;DR

The paper introduces interactive Monte Carlo simulations and a genetic algorithm for educational purposes in thermodynamics and statistical mechanics.

## Contribution

It presents JavaScript and Java programs for teaching concepts like entropy, ensembles, and the Second Law of Thermodynamics through simulations.

## Key findings

- Interactive simulations of argon in the grand-isobaric ensemble allow direct entropy calculation and analysis of vapor–liquid equilibria.
- A genetic algorithm in Java is proposed as a pedagogical tool to explain the Second Law and cumulative selection in biogenesis.
- The programs include microcanonical ensemble analysis of quantized harmonic oscillators and definitions of Boltzmann and Gibbs entropies.

## Abstract

This paper concerns interactive Monte Carlo simulations for adiabatic ensembles and a genetic algorithm to research and educational contexts. In the Introduction, we discuss some concepts of thermodynamics, statistical mechanics and ensembles relevant to molecular simulations. The second and third sections of the paper comprise two programs in JavaScript regarding (i) argon in the grand-isobaric ensemble focusing on the direct calculation of entropy, vapor–liquid equilibria and radial distribution functions and (ii) an ideal system of quantized harmonic oscillators in the microcanonical ensemble for the determination of the entropy and Boltzmann distribution, also including the definition of Boltzmann and Gibbs entropies relative to classical systems. The fourth section is concerned with a genetic algorithm program in Java, as a pedagogical alternative to introduce the Second Law of Thermodynamics, which summarizes artificial intelligence methods and the cumulative selection process in biogenesis.