BIBLIOS

Document type
Journal articles

Document subtype
Full paper

Title
Entropy production inequalities for the Kac Walk

Participants in the publication
Eric A. Carlen (Author)
RUTGERS UNIVERSITY
Maria C. Carvalho (Author)
Dep. Matemática
CMAFcIO
Amit Einav (Author)

Summary
Mark Kac introduced what is now called 'the Kac Walk' with the aim of investigating the spatially homogeneous Boltzmann equation by probabilistic means. Much recent work, discussed below, on Kac's program has run in the other direction: using recent results on the Boltzmann equation, or its one-dimensional analog, the non-linear Kac-Boltzmann equation, to prove results for the Kac Walk. Here we investigate new functional inequalities for the Kac Walk pertaining to entropy production, and introduce a new form of 'chaoticity'. We then show how these entropy production inequalities imply entropy production inequalities for the Kac-Boltzmann equation. This results validate Kac's program for proving results on the non-linear Boltzmann equation via analysis of the Kac Walk, and they constitute a partial solution to the 'Almost' Cercignani Conjecture on the sphere.


Institution
FACULDADE DE CIÊNCIAS DA UNIVERSIDADE DE LISBOA

Where published
Kinetic Theory and Related Models

Publication Identifiers
ISSN - 1937-5093

Publisher
American Institute of Mathematical Sciences (AIMS)



Document Identifiers
DOI - https://doi.org/ doi: 10.3934/krm.2018012

Keywords
Kac Walk chaoticity entropy method entropy production cercignani conjecture.