2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/109462We consider a driven Brownian particle, subject to both conservative and non-conservative applied forces, whose probability evolves according to the Kramers equation. We derive a general fluctuation relation, expressing the ratio of the probability of a given Brownian path in phase space with that of the time-reversed path, in terms of the entropy flux to the heat reservoir. This fluctuation relation implies those of Seifert, Jarzynski and Gallavotti-Cohen in different special cases.Statistical MechanicsOther Condensed Mattertext