Intermediate Thermal Equilibrium Stages in Molecular Dynamics Simulations of two Bodies in Contact

The Zeroth Law of Thermodynamics states that if two systems are in thermal equilibrium with a third one, then they are also in equilibrium with each other. This study explores not only the final state of thermal equilibrium between ideal gases separated by heat-conducting walls, but also the intermediate stages leading up to equilibrium, using classical molecular dynamics simulations. Two- and three-region models with argon atoms are analyzed. Fluctuations, correlations, and temperature distributions are observed, highlighting how heat conduction between regions influences the time to reach equilibrium. This work is distinguished by its detailed analysis of the intermediate stages that occur until the system reaches thermal equilibrium, in accordance with the Zeroth Law of Thermodynamics.