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Generalized Maxwell-Boltzmann, Bose-Einstein, Fermi-Dirac and Acharya-Swamy Statistics and the Polya Urn Model
Robert K. Niven, Marian Grendar
Generalized probability distributions for Maxwell-Boltzmann, Bose-Einstein and Fermi-Dirac statistics, with unequal source probabilities for each level , are obtained by c…
The Polya Urn: Limit Theorems, Polya Divergence, Maximum Entropy and Maximum Probability
Marian Grendar, Robert K. Niven
Sanov's Theorem and the Conditional Limit Theorem (CoLT) are established for a multicolor Polya Eggenberger urn sampling scheme, giving the Polya divergence and the Polya extension…
Combinatorial Information Theory: I. Philosophical Basis of Cross-Entropy and Entropy
Robert K. Niven
This study critically analyses the information-theoretic, axiomatic and combinatorial philosophical bases of the entropy and cross-entropy concepts. The combinatorial basis is show…
q-Exponential Structure of Arbitrary-Order Reaction Kinetics
Robert K. Niven
The rate equation for an arbitrary mth order growth or decay reaction can be expressed in terms of the q-exponential function, with q equal to m. The analysis suggests that a wide…
Constrained Forms of the Tsallis Entropy Function and Local Equilibria
Robert K. Niven
The Lagrangian technique of Niven (2004, Physica A, 334(3-4): 444) is used to determine the constrained forms of the Tsallis entropy function - i.e. Lagrangian functions in which t…
Exact Maxwell-Boltzmann, Bose-Einstein and Fermi-Dirac Statistics
Robert K. Niven
The exact Maxwell-Boltzmann (MB), Bose-Einstein (BE) and Fermi-Dirac (FD) entropies and probabilistic distributions are derived by the combinatorial method of Boltzmann, without St…