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We establish a refined version of the Second Law of Thermodynamics forLangevin stochastic processes describing mesoscopic systems driven byconservative or non-conservative forces and interacting with thermal noise. Therefinement is based on the Monge-Kantorovich optimal mass transport. Generaldiscussion is illustrated by numerical analysis of a model for micron-sizeparticle manipulated by optical tweezers.

Refined Second Law of Thermodynamics for fast random processes