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Thermodynamic non-additivity in disordered systems with extended phase space

100%
Vakarin E., Badiali J.
Open Physics
|
2004
|
vol. 2
|
issue 2
241-253
EN
Non-additivity effects in coupled dynamic-stochastic systems are investigated. It is shown that there is a mapping of the replica approach to disordered systems with finite replica indexn on Tsallis non-extensive statistics, if the average thermodynamic entropy of the dynamic subsystem differs from the information entropy for the probability distribution in the stochastic subsystem. The entropic indexq is determined by the entropy difference ΔS. In the case of incomplete information, the entropic indexq=1−n is shown to be related to the degree of lost information.
2
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A mathematical structure for the generalization of conventional algebra

71%
Kaabouchi A., Nivanen L., Wang Q., Badiali J., Méhauté A.
Open Physics
|
2009
|
vol. 7
|
issue 3
549-554
EN
An abstract mathematical framework is presented in this paper as a unification of several deformed or generalized algebra proposed recently in the context of generalized statistical theories intended to treat certain complex thermodynamic or statistical systems. It is shown that, from a mathematical point of view, any bijective function can in principle be used to formulate an algebra in which the conventional algebraic rules are generalized.
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