On the relation between stochastic thermodynamics and linear irreversible thermodynamics
Abstract:
A wealth of natural phenomena, from the biogeochemical cycles at planetary scales to the transport of molecules along microtubules in the inside of a cell, are all instances of the same archetype in the eye of a thermodynamicist: a subsystem traversed by fluxes of heat and matter with its surroundings. These fluxes are caused by inhomogeneities in quantities such as temperature or concentration. Two main theoretical approaches are available to deal with these situations.
The first framework is phenomenological irreversible thermodynamics, which historically arose as the extension of equilibrium thermodynamics to spatially continuous systems. It deals with systems for which experimental constitutive laws are given for the fluxes that are generated in response to thermodynamic forces. It becomes most powerful when a linear relation between fluxes and thermodynamic forces well approximates the dependence over many orders of magnitude. In fact, in this near-equilibrium regime, powerful statistical results allow for a compact characterization of the thermodynamic behavior in terms of the response coefficients of the fluxes.
The second framework is provided by stochastic thermodynamics, a modern formulation of non-equilibrium statistical mechanics dealing with systems in contact with several heats and particle reservoirs and for which fluctuations play a significant role.
In this thesis, I provide a systematic treatment of the linear regime of stochastic thermodynamics, showing how to recover the properties of linear irreversible thermodynamics, probing their validity when extending the setting to time-dependent systems slightly driven out of equilibrium. Secondly, I show how, borrowing tools from stochastic thermodynamics, we are able to provide microscopic interpretations for thermodynamic quantities appearing in linear irreversible thermodynamics. The explicit objective is to show that the two approaches share the same basic structure, suggesting that systematic coarse-graining procedures could provide an even more direct link in the future.
In the second part of the thesis, I present two case studies on the response to perturbations that are not limited to the linear regime. These problems defy the setting of linear irreversible thermodynamics, yet are treatable using stochastic thermodynamics. The first case study concerns the possibility of enhancing the flux of an enzymatic reaction by using time-dependent control of its inputs. The second case study analyzes the asymmetric relaxation speed of hot and cold states of a diffusive system in an anharmonic potential following a sudden quench.
Dissertation defence jury
Chair:Professor Thomas Schmidt, Université du Luxembourg
Vice-Chair: Professor Etienne Fodor, Université du Luxembourg
Member: Professor Marco Baiesi, Università degli Studi di Padova
Member (Supervisor): Professor Massimiliano Esposito, Université du Luxembourg
Member: Professor Juan M. R. Parrondo, Universidad Complutense de Madrid