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On the energy translation invariance of probability distributions

Q. A. Wang·L. Nivanen·M. Pezeril·A. Le Mehaute
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Abstract

We comment on the problem of energy translation invariance of probability distribution and present some observations. It is shown that a probability distribution can be invariant in the thermodynamic limit if there is no long term interaction or correlation and no relativistic effect. So this invariance should not be considered as a universal theoretical property. Some peculiarities within the invariant $q$-exponential distribution reveal that the connection of the current nonextensive statistical mechanics to thermodynamics might be disturbed by this invariance.

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Q. A. Wang, L. Nivanen, M. Pezeril, A. Le Mehaute. 2002-06-04. On the energy translation invariance of probability distributions. https://arxiv.org/abs/cond-mat/0206043

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