Incomplete nonextensive statistics and the zeroth law of thermodynamics

Abstract

PACS. 05.20.-y -Classical statistical mechanics. PACS. 05.70.-a -Thermodynamics. PACS. 02.50.-r-Probability theory, stochastic process, and statistics.Abstract. On the basis of the entropy of incomplete statistics (IS) and the joint probability factorization condition, two controversial problems existing in IS are investigated, where one is what the correct expression of the internal energy for a composite system is and the other is whether the zeroth law of thermodynamics is true or not. Some new equivalent expressions of the internal energy of a composite system are derived through a precise mathematical calculation. Moreover, a self-consistent calculation is used to expound that the zeroth law of thermodynamics is also suitable for IS, but it can't be proven from theory. Finally, it is pointed out that the generalized zeroth law of thermodynamics and the expressions of the internal energy of a composite system derived in literature are incorrect, because two irrational assumptions have been implicitly introduced.

Tsallis Wavelet Entropy and Its Application in Power Signal Analysis

“…It is well known that Boltzmann-Gibbs statistics (BGS) are inadequate for treating some complex systems [14]. These are systems with complex or long term interactions and correlations, systems showing often distribution laws are different from the usual ones (Gauss, Poisson), systems in chaotic or fractal states and often related to nonextensive phenomena in energy, entropy, heat, and other quantities [15]. In the process of wavelet decomposition, energy leakage exists at each scale, and the leakage of energy invades neighboring scales.…”