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Tsallis Statistics, Statistical Mechanics for Non-extensive Systems and Long-Range Interactions

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A standard assumption of statistical mechanics is that quantities like energy are "extensive" variables, meaning that the total energy of the system is proportional to the system size; similarly the entropy is also supposed to be extensive. Generally, at least for the energy, this is justified by appealing to the short-range nature of the interactions which hold matter together, form chemical bonds, etc. But suppose one deals with long-range interactions, most prominently gravity; one can then find that energy is not extensive. This makes the life of the statistical mechanic much harder. Constantino Tsallis is a physicist who came up with a supposed solution, based on the idea of maximum entropy. One popular way to derive the (canonical) equilibrium probability distribution is the following. One purports to know the average values of some quantities, such as the energy of the system, the number of molecules, the volume it occupies, etc. One then searches for the probability distributio

Tsallis Statistics, Statistical Mechanics for Non-extensive Systems and Long-Range Interactions Notebooks Tsallis Statistics, Statistical Mechanics for Non-extensive Systems and Long-Range Interactions Last update : 07 Jul 2025 12:01 First version : Before 16 July 2004 (maybe 2003?) A standard assumption of statistical mechanics is that quantities like energy are "extensive" variables, meaning that the total energy of the system is proportional to the system size; similarly the entropy is also supposed to be extensive. Generally, at least for the energy, this is justified by appealing to the s

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