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2024 | OriginalPaper | Chapter

Entropy Production Bounds for the Kac Model are Uniform in the Number of Particles

Author : Luís Simão Ferreira

Published in: From Particle Systems to Partial Differential Equations

Publisher: Springer International Publishing

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Abstract

The chapter delves into the intricate relationship between entropy production and equilibrium convergence in Kac's model, focusing on bounds that are uniform in the number of particles. It introduces the concept of entropy production inequalities and their superiority over spectral gap methods. The HWI inequality is highlighted as a powerful tool for deriving entropy power laws. The main results include entropy power laws for both Kac's process and the Boltzmann equation, demonstrating the utility of these techniques in understanding complex systems. The text also provides a detailed exposition of the Wasserstein distance, Fisher information, and the concept of chaos, making it a valuable resource for researchers in mathematical physics and related fields.

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previous chapter The Entropic Journey of Kac’s Model

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Title: Entropy Production Bounds for the Kac Model are Uniform in the Number of Particles
Author: Luís Simão Ferreira
Publisher: Springer International Publishing
Book: From Particle Systems to Partial Differential Equations
Print ISBN: 978-3-031-65194-6

Electronic ISBN: 978-3-031-65195-3

Copyright Year: 2024
DOI: https://doi.org/10.1007/978-3-031-65195-3_5

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