An axiomatic definition is given for the q-gamma function Γq(x),q∈R,q0,x∈R of Tsallis (non-extensive) statistical physics, the continuous analogue of the q-factorial of Suyari [H. Suyari, Physica A 368 (1) (2006) 63], and the q-analogue of the gamma function Γ(x) of Euler and Gauss. A...

The exact forms of the degenerate Maxwell–Boltzmann (MB), Bose–Einstein (BE) and Fermi–Dirac (FD) entropy functions, derived by Boltzmann's principle without the Stirling approximation [R.K. Niven, Physics Letters A, 342(4) (2005) 286], are further examined. Firstly, an apparent paradox in...

This study concerns the use of ethanol as a gasoline (petrol) additive, at levels around 10% by volume ('E10') as well as an 85% blend ('E85'). By detailed reviews of the peer-reviewed and technical literature, five environmental aspects of ethanol enrichment are examined: (1) its purported...

This study introduces the constrained forms of the Shannon information entropy and Kullback–Leibler cross-entropy functions. Applicable to a closed system, these functions incorporate the constraints on the system in a generic fashion, irrespective of the form or even the number of the...