Inhomogeneous Tsallis distributions in the HMF model

Details Inhomogeneous Tsallis distributions in the HMF model Inhomogeneous Tsallis distributions in the HMF model

2010-01-13

arxiv.org/abs/1001.2109v1

Eur. Phys. J. B 76, 581 (2010)

Physics

Condensed Matter

Statistical Mechanics

Scientific paper

We study the maximization of the Tsallis functional at fixed mass and energy in the HMF model. We give a thermodynamical and a dynamical interpretation of this variational principle. This leads to q-distributions known as stellar polytropes in astrophysics. We study phase transitions between spatially homogeneous and spatially inhomogeneous equilibrium states. We show that there exists a particular index q_c=3 playing the role of a canonical tricritical point separating first and second order phase transitions in the canonical ensemble and marking the occurence of a negative specific heat region in the microcanonical ensemble. We apply our results to the situation considered by Antoni & Ruffo [Phys. Rev. E 52, 2361 (1995)] and show that the anomaly displayed on their caloric curve can be explained naturally by assuming that, in this region, the QSSs are polytropes with critical index q_c=3. We qualitatively justify the occurrence of polytropic (Tsallis) distributions with compact support in terms of incomplete relaxation and inefficient mixing (non-ergodicity). Our paper provides an exhaustive study of polytropic distributions in the HMF model and the first plausible explanation of the surprising result observed numerically by Antoni & Ruffo (1995). In the course of our analysis, we also report an interesting situation where the caloric curve presents both microcanonical first and second order phase transitions.

Affiliated with

Also associated with

No associations

Rating

Inhomogeneous Tsallis distributions in the HMF model 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 Inhomogeneous Tsallis distributions in the HMF model, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Inhomogeneous Tsallis distributions in the HMF model will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-525021