0 Remark on the Second Principle of Thermodynamics

All presently available results lead to the conclusion that nonextensivity, in the sense of nonextensive statistical mechanics (i.e., q = 1), does not modify anything to the second principle of thermodynamics, which therefore holds in the usual way. Moreover, some claims in the literature that this principle can be violated for specific anomalous systems (e.g., granular materials) can be shown to be fallacious. One recent such example is analyzed, and it is suggested how q = 1 distributions could in fact restore the validity of macroscopic time irreversibility, a cornerstone of our present understanding of nature. The Second Principle of Thermodynamics, i.e., time irreversibility of the macroscopic world, appears to be one of the most solid laws of theoretical physics. Usual statistical mechanics , i.e., Boltzmann-Gibbs statistical mechanics, is consistent with this principle through the celebrated H-theorem. We address here what happens with this principle within the nonextensive statistical mechanics proposed in 1988 [1] and characterized by an entropic index q (the particular case q = 1 recovers standard Boltzmann-Gibbs statistical mechanics). The answer seems to be very simple: no hope for moto perpetuo within this formalism! Indeed, the H-theorem appears to be q-invariant, more precisely, excepting for very quick microscopic fluctuations, S q cannot decrease (increase) with time if q > 0 (q < 0), a fact which is consistent with the concavity (convexity) of S q , with regard to the set of probabilities , for q > 0 (q < 0) (hence, S q is respectively maximal and minimal for q > 0 and 1