Thermostated Kac models

We consider a model of N particles interacting through a Kac-style collision process, with m particles among them interacting, in addition, with a thermostat. When m = N, we show exponential approach to the equilibrium canonical distribution in terms of the L2 norm, in relative entropy, and in the Gabetta-Toscani-Wennberg (GTW) metric, at a rate independent of N. When m < N , the exponential rate of approach to equilibrium in L2 is shown to behave as m/N for N large, while the relative entropy and the GTW distance from equilibrium exhibit (at least) an "eventually exponential” decay, with a rate scaling as m/N^2 for large N. As an allied project, we obtain a rigorous microscopic description of the thermostat used, based on a model of a tagged particle colliding with an infinite gas in equilibrium at the thermostat temperature. These results are based on joint work with Federico Bonetto, Michael Loss and Hagop Tossounian.

Level thesis:degree_level

Doctoral

Department dc:contributor.department

Mathematics

Grantor dc:publisher

Georgia Institute of Technology

Year dc:date.issued

2015

Author dc:creator

• Vaidyanathan, Ranjini

Advisor dc:contributor.advisor

• Bonetto, Federico

Committee members dc:contributor.committeemember

• Loss, Michael
• de la Llave, Rafael
• Harrell, Evans
• Wiesenfeld, Kurt

• Kinetic theory
• Spectral gap
• Heat bath

Language dc:language.iso

en_US

Handle dc:identifier.uri

http://hdl.handle.net/1853/54446

OAI identifier oai:identifier

oai:repository.gatech.edu:1853/54446