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

TL;DR

The problem addressed is understanding how two thermally coupled bodies approach equilibrium in molecular dynamics, not just the final state but the intermediate stages. The authors implement classical MD with Lennard-Jones argon in two configurations—a two-region and a three-region system—to observe heat transfer through diathermal inner walls while outer walls act adiabatically, analyzed with temperature fluctuations, correlations, and distributions. Key findings show that a simple two-region system equilibrates with near-exponential relaxation (e.g., $C(t) \sim e^{-t/\tau}$ with $\tau$ around 662 time steps), while introducing a central intermediary region yields slower, multi-stage relaxation, bimodal temperature distributions, and strong anti-correlations between end regions; the middle region acts as a heat transporter and bottleneck ($\tau$ values: $\tau_{2\text{region}} \approx 662$, $\tau_{\text{lateral}} \approx 1669$, $\tau_{\text{middle}} \approx 216$). This work highlights non-trivial pathways to thermal equilibration in finite systems and refines the dynamical interpretation of the Zeroth Law by exposing intermediate metastable states and interfacial bottlenecks. The findings have implications for microscopic heat-transfer design and fundamental thermodynamics in non-equilibrium contexts.

Abstract

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.

Figures (12)

• Figure 1: (a) Simulation box with three walls separating the system into two regions (left and right), each containing 400 argon atoms. (b) Simulation box with four walls separating the system into three regions (left, middle, and right), with 400 argon atoms in the lateral regions and 100 atoms in the central region.
• Figure 2: Evolution of temperature for a system with two and three regions in contact. Comparative analysis of temperature evolution in the lateral regions for Cases 1 and 2.
• Figure 3: Evolution of temperature for a system with three regions in contact.Temperature profiles for each region in Case 2 (top). The bottom panel presents a comparison between the average temperature of the lateral regions, the global average temperature, and the temperature in the middle region.
• Figure 4: Evolution of the temperature means for cases 1 and 2. Comparative Evolution of the average temperature for a system with two and three regions in contact.
• Figure 5: Conditional temperature volatility (dT) for two and three regions in contact. The triangular points correspond to Case 1 and the circular points to Case 2. The subgraph shows the average value for Case 1 (average of the two regions) and Case 2 (average of the ends and the three regions together).