arXiv subjects
Publications and source records attributed to C. J. Ou.
This is a note showing that, contrary to our lasting belief, the nonadditivity X(1+2)=X(1)+X(2)+αX(1)X(2) is not a true physical property. αin this expression cannot be unique for a given system. It unavoidably depends on how one mathematically divides the system and cannot be used to characterize nonadditivity. As a matter of fact, its use is mathematically inconsistent.
We provide a counterexample to show that the generic form of entropy S(p)=sum_i g(p_i) is not always stable against small variation of probability distribution (Lesche stability) even if is concave function on [0,1] and analytic on ]0,1]. Our conclusion is that the stability of such a generic functional needs more hypotheses on the property of the function g, or in other words, the stability of entropy cannot be discussed at this formal stage.
In this paper, we give a new method for proving the Lesche stability of several functionals(Incomplete entropy, Tsallis entropy, κ- entropy, Quantum-Group entropy). We prove also that the Incomplete q - expectation value and Renyi entropy for (0 < q < 1) are α- stable for all (0 <α<= q). Finally, we prove that the Incomplete q - expectation value is α- stable for all 0 <α<=1.
In this work, we consider a recently proposed entropy S (called varentropy) defined by a variational relationship dI=beta*(d - ) as a measure of uncertainty of random variable x. By definition, varentropy underlies a generalized virtual work principle =0 leading to maximum entropy d(I-beta* )=0. This paper presents an analytical investigation of this maximizable entropy for several distributions such as stretched exponential distribution, kappa-exponential distribution and Cauchy distribution.