Project R-11130

GENERAL ASPECTS ABOUT STOCHASTIC THERMODYNAMICS: STOCHASTIC IMPEDANCE AND THERMODYNAMICS OF BROWNIAN PARTICLES. (Research)

This PhD project aims at studying distinct innovative and relevant aspects about stochastic thermodynamics. In the first work package, we consider the use of entropy production as a tool for characterizing phase transitions. Although promising, this study still requires further studies, including an extension for systems with different symmetries and properties and for the analysis of other quantities. We intend to verify/establish whether phase transitions present well-defined signatures when analyzed from the perspective of uncertainty relations and/or Jarzynski and Crooks type relationships. The second work package aims at considering different versions for periodic stochastic pumps. As a first step we consider systems whose coupling with the different reservoirs is periodically modulated in time. Such a driving is in contrast with the usual case (eg. time oscillating temperatures or chemical potentials), mainly by the existence of different Onsager coefficients and reciprocity relations. This concept has been considered for discrete systems described by a master equation, and we intend to generalize this for Brownian particles. Our study will encompass the influence of period as well as the over-damped and under-damped Brownian particles. We intend to obtain their (nonequilibrium) thermodynamic properties as well as to establish general considerations about stochastic efficiency. The third work package of this project aims at advancing in the study of stochastic impedance. Recently, the concept of impedance was introduced in a stochastic setting, consisting of an electron transport through a singlelevel quantum dot connected to two electron reservoirs for fixed temperature and energy levels. Although a quite rudimentary setup (without any interaction between the electrons), a rich behavior is already observed for the impedance. Here we intend to elaborate on these findings in a more general setting, for example by considering other quantities such as energy, heat and work.

01 March 2021 - 31 December 2023