Fluctuations dynamiques et thermodynamique stochastique des systèmes conduits périodiquement

par Lydia Chabane

Projet de thèse en Physique

Sous la direction de Gatien Verley.

Thèses en préparation à Paris Saclay , dans le cadre de École doctorale Physique en Île-de-France (Paris) , en partenariat avec Laboratoire de physique théorique (Orsay, Essonne) (laboratoire) et de Université Paris-Sud (établissement de préparation de la thèse) depuis le 01-10-2018 .

  • Titre traduit

    Dynamical fluctuations and stochastic thermodynamics of periodically driven systems

  • Résumé

    Stochastic thermodynamics aims at describing small and irreversible systems that are highly influenced by thermal fluctuations of their environment [Seifert 2012] . Such systems are for instance molecular motors, stretched DNA molecules manipulated by optical tweezers, Brownian engines, biochemical reaction networks, etc. They are usually modeled as continuous time Markov processes, either in discrete or continuous space. Recent investigations on systems driven into a non-equilibrium stationary state (NESS) have been particularly fruitful for systems modeled by continuous time Markov chains: It is possible now to reveal systematically the conservation laws of systems of arbitrary complexity [Polettini,Bulnes-Cuetara & Esposito 2016] ; to characterize the fluctuations of dynamical observables (e.g. energy fluxes, activity) in small systems using large deviation theory and path ensemble techniques [Chetrite & Touchette 2015] ; to understand the nonlinear behavior of currents using the concept of non-equilibrium conductance matrix [Vroylandt,Lacoste & Verley 2018] ; to re-interpret the fluctuations-dissipation theorem as an inequality in the context of NESS [Gingrich,Horowitz,Perunov & England 2016] ; or to use such inequalities to constrain the output power and efficiency of machines, extending the concept of degree of coupling introduced by Kedem-Caplan in the sixties. Most of these results only hold for systems in stationary states and not for “Time Periodic States” (TIPS). Exploring experimentally the predictions of stochastic thermodynamics for non-equilibrium systems often requires to drive them periodically [Proesmans,Dreher,Gavrilov,Bechhoefer & Van den Broeck 2016]. Along the same line, energy converters often operate periodically to deliver mechanical or chemical work, sometimes by crossing a phase transition. Being able to study these phenomena or experimental systems requires a specific theory for TIPS. The goal of this thesis is to extend former works obtained for NESS to TIPS. It will use large deviation theory to generalize the concept of non-equilibrium conductance which has many interesting potential applications.