Abstract
Dynamics for a generalized thermodynamics due to Tsallis is formulated based on a new Langevin equation, with classical driving force and nonclassical multiplicative noise. As applications, the Kramers problem (thermal activation rate over a potential barrier) and anomalous Brownian motion are considered within the framework of the generalized thermodynamics. The dynamics is generalized further by treating temperature as a stochastic variable, leading to a Langevin formulation of simulated tempering for efficient Monte-Carlo sampling and optimization.
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