Starts 16 Jun 2022 11:00
Ends 16 Jun 2022 12:00
Central European Time
Hybrid Seminar
room 128, SISSA (via Bonomea 265) + Zoom


Carlos Meija Monasterio
(TU-Madrid)


Abstract:
Demonstrating how microscopic dynamics cause large systems to approach thermal equilibrium remains an elusive, longstanding, and actively pursued goal of statistical mechanics. Statistical mechanics teaches that for systems described by a Hamiltonian $H$, the thermal states are those described by the canonical Boltzmann relation $\rho = Z^{-1} \exp(-\beta H)$. This follows from original arguments of Maxwell, marginal distributions that arise from microcanonical ensembles, and the properties of the maximum entropy of limiting states. While such statistical arguments identify the thermal state, they provide no insight into the problem of how the microscopic dynamics of diverse large systems each lead towards equilibrium from an arbitrary initial state. We explore this issue by studying the convergence toward thermal equilibrium of Hamiltonian (and mechanical) systems of interacting particles in contact with a bath of other systems. We focus on interactions that occur through collisions and explore the conditions under which the system reaches equilibrium after repeated and random interactions with the bath’s degrees of freedom. If the system is in contact with a bath out of equilibrium, equilibration of the system is always attained when the coupling with the bath is weak. Beyond the weak-coupling limit, equilibration is not granted and limiting state strongly depends on the details of the bath’s energy distribution.