We consider maximum entropy solutions to Nonlinear Fokker–Planck equations within general thermostatistical formalisms. We show that the family of generalized nonextensive entropies introduced by Tsallis is the only one that has an associated family of nonlinear Fokker–Planck equations...

We construct entropy functionals which discriminate the measures which converge to equilibrium in the case of shifts dynamical systems. In particular for K-shifts it is proved that some functionals associated to them decrease monotonically to zero.

Thermodynamics’ first law (TFL), although undoubtedly true because of its many verified consequences, rests on a rather weak experimental foundation in the sense that, as pointed out by Pippard, its path-independent aspect cannot be said to have been directly verified. From the theoretical...