Alain Le Méhauté

On the generalized entropy pseudoadditivity for complex systems

We show that Abes general pseudoadditivity for entropy prescribed by thermal equilibrium in nonextensive systems holds not only for entropy, but also for energy. The application of this general pseudoadditivity to Tsallis entropy tells us that the factorization of the probability of a composite system into a product of the probabilities of the subsystems is just a consequence of the existence of thermal equilibrium and not due to the independence of the subsystems.

Unnormalized nonextensive expectation value and zeroth law of thermodynamics

Abstract On the basis of complete distribution normalization Tr ρ =1 and unnormalized average energy E= Tr ρ q H , we show an attempt to establish the zeroth law of thermodynamics within the framework of nonextensive statistical mechanics for canonical ensemble. The first law of thermodynamics and the statistical interpretation of heat and work are discussed.

Generalized blackbody distribution within the dilute gas approximation

We consider the application of Tsallis’ generalized statistical mechanics to systems of quantum particles (fermions or bosons). An approach due to Buyukkilic et al. to find analytic formulae for quantum distribution functions and its application to generalized blackbody radiation is discussed. Generalized blackbody laws (Stefan–Boltzmann law, Rayleigh–Jeans law and Wien empirical distribution law) are proposed.

MAXIMIZABLE INFORMATIONAL ENTROPY AS A MEASURE OF PROBABILISTIC UNCERTAINTY

In this work, we consider a recently proposed entropy S defined by a variational relationship

Nonextensive boson gas and specific heat of 4He superfluid

dI=d\bar{x}-\overline{dx}

A mathematical structure for the generalization of conventional algebra

as a measure of uncertainty of random variable x. The entropy defined in this way underlies an extension of virtual work principle

CONTRIBUTION OF NON INTEGER INTEGRO-DIFFERENTIAL OPERATORS (NIDO) TO THE GEOMETRICAL UNDERSTANDING OF RIEMANN'S CONJECTURE-(I)

\overline{dx}=0

Contribution of Non Integer Integro-Differential Operators (NIDO) to the geometrical understanding of Riemann's conjecture-(II)

leading to the maximum entropy

Nonextensive distribution and factorization of the joint probability

d(I-\bar x)=0

Stability of incomplete entropy and incomplete expectation

. This paper presents an analytical investigation of this maximizable entropy for several distributions such as the stretched exponential distribution, κ-exponential distribution, and Cauchy distribution.