Stochastic thermodynamics of collisional thermal machines and phase transition

Abstract

Non-equilibrium thermodynamics has become one of the main areas of modern statistical mechanics and presenting several applications, such as in phase transitions, biological systems, chemical reactions, engineered systems and others. In the context of small-sized systems (nanometric scale) stochastic thermodynamics was developed and describes energy transformations from the framework of Markov process, hence constituting a relevant toolbox in modern statistical physics. In all these cases, entropy production plays a central role, discerning not only the occurrence or not of certain process but also how energy can be converted into useful work and vice-versa. This PHD thesis is aimed at studying such ideas in the framework of stochastic thermodynamics. In the first part of this thesis, we introduce a strategy for optimizing the performance of Brownian engines, based on a collisional approach. General (and exact) expressions for thermodynamic properties and their optimized values are obtained, irrespective of the driving forces, duration of each stage, the temperatures of reservoirs and protocol to be maximized. Distinct routes for the engine optimization, including maximizations of output power and efficiency with respect to the asymmetry, force and both of them are investigated. The idea of conveniently adjusting/choosing intermediate reservoirs as a strategy for optimizing the performance of a quantum-dot machine sequentially exposed to distinct reservoirs at each stage was also studied, whose thermodynamic quantities (including power and efficiency) can be exactly obtained, irrespective to the number of stages and certain advantages about increasing the number of intermediate stages were discussed. Lastly, we show that entropy production not only locates and distinguishes continuous and first-order phase transitions, but their fluctuations are important in the vicinity of first-order phase transitions and depends on the interplay between observation time and inter-phase tunneling times.