Diffusione Browniana in prossimità di un muro: Trasporto delle particelle e Termodinamica Stocastica

Brownian dynamics is a well known branch of Statistical Physics, which has been the subject of huge interest throughout the last century. Brownian ratchets, gyrators, mesoscopic heat-engines, and stochastic thermodynamics are only few of the many fields which have Brownian motion as a common denominator. I will explain the basic features of this physical phenomenon and introduce the standard model for Brownian motion in form of so-called (overdamped) Langevin and Fokker-Planck equations. Afterwards, the focus will be on the rectification of thermal noise under non-equilibrium conditions. Starting with the simple example of a flashing ratchet, I will then present a recently discovered rectification mechanism, which features a Brownian par- ticle at a (hard-wall) boundary in an anisotropic thermal environment. The sorting of particles of di↵erent sizes will be then deeply discussed as one of the important results of the model leading us to many interesting considerations. Afterwards, the discussion will lead us to the stochastic thermodynamics of this set-up, demonstrating that it can operate either as a mesoscopic heat engine or as a refrigerator machine, depending on external control parame- ters. Lastly, we analyse the e ciency and its fluctuations through the theory of large deviations for such device in the regime where it behaves as an heat engine. Finally, I will present some examples and practical uses of this tech- nology as a conclusion.