Numerical Analysis of D-Entropy in Interacting Particle Systems: Insights into Energy Redistribution in Classical Mechanics

This study analyzes a system of interacting particles influenced by gravitational forces and internal Lennard-Jones interactions, focusing on energy redistribution and introducing D-Entropy as a measure of internal energy changes. Numerical simulations reveal that, despite overall energy conservation, significant initial fluctuations in individual energy components occur due to complex interactions. The system shows dynamic energy redistribution, particularly as it transitions from a far-from-equilibrium state to a stable configuration, with D-Entropy capturing periods of rapid energy exchange followed by reduced fluctuations.Particle trajectories exhibit complex behaviors, including deviations and oscillations driven by gravitational and Lennard-Jones forces. Nonlinear interactions significantly impact energy redistribution and system stability. The results demonstrate the utility of D-Entropy in quantifying energy changes and provide insights into the thermodynamic evolution of structured bodies.Future research will incorporate dissipative forces, explore other interaction potentials, and scale up the system to study collective effects and phase transitions. These findings have potential applications in materials science, astrophysics, and other fields involving dynamic structured systems.