Physics – Condensed Matter – Statistical Mechanics
Scientific paper
2004-12-13
Physical Review E 71, 046144 (2005)
Physics
Condensed Matter
Statistical Mechanics
14 pages including 3 figures
Scientific paper
10.1103/PhysRevE.71.046144
It is by now well known that the Boltzmann-Gibbs (BG) entropy $S_{BG}=-k\sum_{i=1}^W p_i \ln p_i$ can be usefully generalized into the entropy $S_q=k (1-\sum_{i=1}^Wp_i^{q}) / (q-1)$ ($q\in \mathcal{R}; S_1=S_{BG}$). Microscopic dynamics determines, given classes of initial conditions, the occupation of the accessible phase space (or of a symmetry-determined nonzero-measure part of it), which in turn appears to determine the entropic form to be used. This occupation might be a uniform one (the usual {\it equal probability hypothesis} of BG statistical mechanics), which corresponds to $q=1$; it might be a free-scale occupancy, which appears to correspond to $q \ne 1$. Since occupancies of phase space more complex than these are surely possible in both natural and artificial systems, the task of further generalizing the entropy appears as a desirable one, and has in fact been already undertaken in the literature. To illustrate the approach, we introduce here a quite general entropy based on a distribution of $q$-indices thus generalizing $S_q$. We establish some general mathematical properties for the new entropic functional and explore some examples. We also exhibit a procedure for finding, given any entropic functional, the $q$-indices distribution that produces it. Finally, on the road to establishing a quite general statistical mechanics, we briefly address possible generalized constraints under which the present entropy could be extremized, in order to produce canonical-ensemble-like stationary-state distributions for Hamiltonian systems.
Tsallis Constantino
Tsekouras Giorgos-Artemios
No associations
LandOfFree
Generalized entropy arising from a distribution of q-indices does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Generalized entropy arising from a distribution of q-indices, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Generalized entropy arising from a distribution of q-indices will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-115293