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Driven Soft Matter: Entropy Production and the Fluctuation-Dissipation Theorem

Entropy and the fluctuation-dissipation theorem are at the heart of statistical mechanics near equilibrium. Driving a system beyond the linear response regime leads to (i) the breakdown of the fluctuation-dissipation theorem and (ii) a nonzero entropy production rate. We show how both phenomena are related using the general framework of stochastic thermodynamics suitable for soft matter systems governed by stochastic dynamics and driven through nonconservative forces or external flows. In particular, the excess of the fluctuation-dissipation theorem in a nonequilibrium steady state compared to equilibrium is related to total entropy production. Alternative recent derivations of generalized fluctuation-dissipation theorems are sketched and related to each other. The theory is illustrated for two systems: a driven single colloidal particle and systems driven through simple shear flow.