Thermodynamics plays a fundamental role in all branches of physics and in many other fields of science and technology. The theory is particularly well established for macroscopic systems at or close to equilibrium. In the last 25 years, however, very significant progress has been made in our understanding of a vast variety of nonequilibrium phenomena, and it is now clear that, under certain conditions and for certain dynamics, a consistent (statistical, in particular) description can be established for systems driven arbitrarily far away from equilibrium.Nonetheless, neither a complete description of nonequilibrium states nor a full characterization of transport processes is available, as the system state appears to strongly depend on the nature of the constraints acting on it, and on many other details of the dynamics. In particular, at present there is no universally accepted generalization of the equilibrium thermodynamic potentials, suitable to describe the state probability distri...
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