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Fluctuations and response of nonequilibrium systems
Gatien Verley, doctorant - Ph.D student Crédits : ESPCI ParisTech In recent years, a broad number of works have shed light on the nature of irreversibility of nonequilibrium phenomena, have permited to redefine quantities such as work or entropy production at the level of trajectories, and to enlight their symmetries through the fluctuation theorems.
During this thesis, we focused on these results in a purely classical and Markovian framework.
We have unified the various formulations of the generalized fluctuation dissipation theorem around steady and unsteady nonequilibrium state by identifying the various sources of irreversibility and by making them appear in the system response. We have tried to link the fluctuation theorems with the theory of linear response which was possible using a generalization of the relation of Hatano and Sasa.
In doing so, we found that different functionals verified symmetry properties similar to the fluctuation theorem for total entropy production. The study of the generalization of Hatano and Sasa relation led us to an inequality of the same type as the Clausius inequality. This new inequality gives a lower bound for the system entropy production during transition between non-stationary states, as the Clausius inequality do for transitions between equilibrium states.
We have illustrated these ideas on a few simple cases analytical or numerical and in an experiment where we manipulate magnetic colloids.
In these experiments, a Crooks relation is expected for a system with spacelly dependant diffusion coefficient, allowing to consider new tests of stochastic thermodynamics.