To: Stan who wrote (1197 ) 7/22/2014 5:03:28 AM From: S. maltophilia 1 RecommendationRecommended By
Read Replies (1) | Respond to Following the links, I found some clarificationextensivity is introduced early in most textbooks on thermodynamics and statistical physics. The requirement that the entropy be additive establishes the form of the Boltzmann-Gibbs distribution via a straightforward argument. Recently, Tsallis [1] has proposed a generalization of Boltzmann-Gibbs thermostatistics by introducing a family of generalized entropy functionals with a single parameter q . The proposed generalization is best described by the following two axioms:Axiom 1 The entropy functional associated with a probability distribution f(z ) is Axiom 2 The experimentally measured value of a phase function g(z ) is given by the q-expectation value, Sq [f ] reduces to the Boltzmann-Gibbs entropy in the limit as q ® 1, Sq [f ], given by Eq. (1), subject to the preservation of various linear global functionals of f (z ). By Tsallis' second postulate, Eq. (2), these are given by i ranges from 1 to the number of conserved quantities n . We are thus led to the variational principle, i 's are Lagrange multipliers. It is an elementary exercise to verify that this yields the equilibrium distribution function n constants li are then determined by the n Eqs. (4) which may be written normalize the q -expectation values as follows:
