{"id":{"repo_id":"gatech","oai_identifier":"oai:repository.gatech.edu:1853/54446"},"canonical_url":"https://search.dev.ndltd.org/etd/gatech/oai:repository.gatech.edu:1853/54446","repository":{"repo_id":"gatech","name":"Georgia Tech","base_url":"https://repository.gatech.edu/server/oai/request"},"display":{"title":"Thermostated Kac models","abstract":"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.","abstract_html":"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 &lt; 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 &quot;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.","abstract_has_math":false,"creators":["Vaidyanathan, Ranjini"],"institution":"Georgia Institute of Technology","degree_name":null,"degree_level":"Doctoral","degree_discipline":null,"degree_department":"Mathematics","school":null,"contributors":[],"advisors":["Bonetto, Federico"],"committee_chairs":[],"committee_members":["Loss, Michael","de la Llave, Rafael","Harrell, Evans","Wiesenfeld, Kurt"],"year":2015,"date_issued":"2015-11-16","date_published":"2015-11-16","updated_at":"2026-07-27T19:51:09Z","subjects":["Kinetic theory","Spectral gap","Heat bath"],"languages":["en_US"],"rights":[],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"http://hdl.handle.net/1853/54446","outbound_label":"Handle","outbound_source":"dc:identifier.uri"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor.advisor","label":"Advisor","values":["Bonetto, Federico"]},{"key":"dc:contributor.committeemember","label":"Committee Member","values":["Loss, Michael","de la Llave, Rafael","Harrell, Evans","Wiesenfeld, Kurt"]},{"key":"dc:contributor.department","label":"Department","values":["Mathematics"]},{"key":"dc:creator","label":"Author","values":["Vaidyanathan, Ranjini"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date.accessioned","label":"Dc Date Accessioned","values":["2016-01-07T17:38:44Z"]},{"key":"dc:date.available","label":"Dc Date Available","values":["2016-01-07T17:38:44Z"]},{"key":"dc:date.issued","label":"Date","values":["2015-11-16"]},{"key":"dc:publisher","label":"Institution","values":["Georgia Institute of Technology"]},{"key":"dc:type","label":"Dc Type","values":["Text"]},{"key":"thesis:degree_level","label":"Degree Level","values":["Doctoral"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["Kinetic theory","Spectral gap","Heat bath"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:language.iso","label":"Language (ISO)","values":["en_US"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier.uri","label":"Identifier URI","values":["http://hdl.handle.net/1853/54446"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description.abstract","label":"Abstract","values":["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."]},{"key":"dc:description.degree","label":"Dc Description Degree","values":["Ph.D."]},{"key":"dc:format.mimetype","label":"Dc Format Mimetype","values":["application/pdf"]},{"key":"dc:title","label":"Title","values":["Thermostated Kac models"]}]}],"canonical_facts":{"dc:contributor.advisor":["Bonetto, Federico"],"dc:contributor.committeemember":["Loss, Michael","de la Llave, Rafael","Harrell, Evans","Wiesenfeld, Kurt"],"dc:contributor.department":["Mathematics"],"dc:creator":["Vaidyanathan, Ranjini"],"dc:date.accessioned":["2016-01-07T17:38:44Z"],"dc:date.available":["2016-01-07T17:38:44Z"],"dc:date.issued":["2015-11-16"],"dc:description.abstract":["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."],"dc:description.degree":["Ph.D."],"dc:format.mimetype":["application/pdf"],"dc:identifier.uri":["http://hdl.handle.net/1853/54446"],"dc:language.iso":["en_US"],"dc:publisher":["Georgia Institute of Technology"],"dc:subject":["Kinetic theory","Spectral gap","Heat bath"],"dc:title":["Thermostated Kac models"],"dc:type":["Text"],"thesis:degree_level":["Doctoral"]},"updated_at":"2026-07-27T19:51:09Z"}