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These regimes are linked numerically to the transition from Gauss-like to Boltzmann-like speed distributions. Furthermore, the different evolution regimes are obtained analytically through velocity-space diffusion analysis. From these calculations, the asymptotic root mean square of speed, initial plateau, and the growth\/decay rates for an intermediate number of collisions are determined in terms of the system parameters. The analytical calculations match the numerical experiments and point to a dynamical mechanism for \u201cthermalization,\u201d where inelastic collisions and a high-dimensional phase space lead to a bounded diffusion in the velocity space toward a stationary distribution function with a kind of \u201creservoir temperature\u201d determined by the boundary oscillation amplitude and the restitution coefficient.<\/jats:p>","DOI":"10.1063\/1.5120023","type":"journal-article","created":{"date-parts":[[2019,10,11]],"date-time":"2019-10-11T15:50:33Z","timestamp":1570809033000},"update-policy":"https:\/\/doi.org\/10.1063\/aip-crossmark-policy-page","source":"Crossref","is-referenced-by-count":1,"title":["Dynamical thermalization in time-dependent billiards"],"prefix":"10.1063","volume":"29","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-0125-9033","authenticated-orcid":false,"given":"Matheus","family":"Hansen","sequence":"first","affiliation":[{"name":"Instituto de F\u00edsica, Universidade de S\u00e3o Paulo 1 , S\u00e3o Paulo CEP 05508-090, SP, Brazil"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-2607-9760","authenticated-orcid":false,"given":"David","family":"Ciro","sequence":"additional","affiliation":[{"name":"Instituto de Astronomia Geof\u00edsica e Ci\u00eancias Atmosf\u00e9ricas, Universidade de S\u00e3o Paulo 2 , S\u00e3o Paulo CEP 05508-090, SP, Brazil"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-1748-0106","authenticated-orcid":false,"given":"Iber\u00ea L.","family":"Caldas","sequence":"additional","affiliation":[{"name":"Instituto de F\u00edsica, Universidade de S\u00e3o Paulo 1 , S\u00e3o Paulo CEP 05508-090, SP, Brazil"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-8224-3329","authenticated-orcid":false,"given":"Edson D.","family":"Leonel","sequence":"additional","affiliation":[{"name":"Departamento de F\u00edsica, UNESP 3 , Rio Claro CEP 13506-900, SP, Brazil"}]}],"member":"317","published-online":{"date-parts":[[2019,10,11]]},"reference":[{"key":"2023063022212254200_c1","doi-asserted-by":"publisher","first-page":"7973","DOI":"10.1088\/0305-4470\/33\/44\/309","volume":"33","year":"2000","journal-title":"J. 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