From Deterministic Trajectories to Probabilistic Descriptions

Fernando C. Pérez-Cárdenas

Staff Scientist
Vitreous State Laboratory
at The Catholic University of America  

Wed, October 12, 2022 - 4:00 PM


I will present simulations illustrating the evolution of simple, small multi-particle systems with deterministic dynamics. It will be shown that, from a coarse-grained viewpoint, a system’s evolution from unlikely to more typical configurations displays apparent irreversibility. (In contrast, from a microscopic point of view, where we have a complete knowledge of the state of the system, the entropy remains constant.) In accordance with Boltzmann’s H-theorem, it is with the introduction of a probabilistic element into the description of the dynamics of an isolated system that we obtain a non-decreasing entropy, as required by the second law of thermodynamics. The approach followed allows us to discuss concepts such as coarse-grained entropy, typicality, and irreversibility, and to distinguish between an effective and a theoretical maximum equilibrium entropy.

 

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