Convergence to the equilibrium state for Bose-Einstein 1-D Kac grazing limit model
Radjesvarane Alexandre, Jie Liao, Chunjin Lin
TL;DR
This paper investigates the exponential convergence to equilibrium in a quantum Kac model for Bose-Einstein particles, employing entropy methods and numerical simulations to establish decay rates.
Contribution
It introduces a detailed entropy analysis to prove exponential decay to equilibrium in the Bose-Einstein quantum Kac model, with numerical validation.
Findings
Exponential decay rate of solutions established
Entropy production analysis used for convergence proof
Numerical simulations support theoretical results
Abstract
The convergence to the equilibrium of the solution of the quantum Kac model for Bose-Einstein identical particles is studied in this paper. Using the relative entropy method and a detailed analysis of the entropy production, the exponential decay rate is obtained under suitable assumptions.The theoretical results are further illustrated by numerical simulations.
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Taxonomy
TopicsAdvanced Thermodynamics and Statistical Mechanics · Gas Dynamics and Kinetic Theory · Optical properties and cooling technologies in crystalline materials