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We review generalized Fluctuation-Dissipation Relations which are valid under general conditions even in ``non-standard systems, e.g. out of equilibrium and/or without a Hamiltonian structure. The response functions can be expressed in terms of suitable correlation functions computed in the unperperturbed dynamics. In these relations, typically one has nontrivial contributions due to the form of the stationary probability distribution; such terms take into account the interaction among the relevant degrees of freedom in the system. We illustrate the general formalism with some examples in non-standard cases, including driven granular media, systems with a multiscale structure, active matter and systems showing anomalous diffusion.
We extend certain basic and general concepts of thermodynamics to discrete Markov systems exchanging work and heat with reservoirs. In this framework we show that the celebrated Clausius inequality can be generalized and becomes an equality, signific
As shown by early studies on mean-field models of the glass transition, the geometrical features of the energy landscape provide fundamental information on the dynamical transition at the Mode-Coupling temperature $T_d$. We show that active particles
The fluctuation-dissipation relation is usually formulated for a system interacting with a heat bath at finite temperature in the context of linear response theory, where only small deviations from the mean are considered. We show that for an open qu
These notes are based on lectures given during the Summer School `Active matter and non-equilibrium statistical physics, held in Les Houches in September 2018. In these notes, we have merged our lectures into a single chapter broadly dedicated to `No
We combine the shear-transformation-zone (STZ) theory of amorphous plasticity with Edwards statistical theory of granular materials to describe shear flow in a disordered system of thermalized hard spheres. The equations of motion for this system are