The q-deformed exponential and logarithmic functions are introduced. Their properties are studied. They form the basis to define the q-exponential families. The notion of escort probability distributions is explained. The q-Gaussian and the q-Maxwellian are given as examples. The relevance of the q-deformed exponential family for closed systems of classical mechanics is demonstrated.
KeywordsLogarithmic Function Exponential Family Multiplicative Noise Dual Exponential Function Average Kinetic Energy
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