Physical peculiarities of divergences emerging in q-deformed statistics

Abstract

It was found in [Europhysics Letters {\bf 104}, (2013), 60003] that classical Tsallis theory exhibits poles in the partition function $\mathcal{Z}$ and the mean energy $<\mathcal{U}>$. These occur at a countably set of the q-line. We give here, via a simple procedure, a mathematical account of them. Further, by focusing attention upon the pole-physics, we encounter interesting effects. In particular, for the specific heat, we uncover hidden gravitational effects.

21 pages, 3 figures. Title has changed. Text has changed

References in corpus (9)

• K*(892)${}^0$ and $\Phi$(1020) production in Pb-Pb collisions at $\sqrt{s_{\mathrm{NN}}}$ = 2.76 TeV
• Nuclear modification factors of phi mesons in d+Au, Cu+Cu and Au+Au collisions at sqrt(S_NN)=200 GeV
• Lynden-Bell and Tsallis distributions for the HMF model
• Convolution of Ultradistributions, Field Theory, Lorentz Invariance and Resonances
• Nonextensivity at the edge of chaos of a new universality class of one-dimensional unimodal dissipative maps
• Continuous transition from the extensive to the non-extensive statistics in an agent-based herding model
• Possible Divergences in Tsallis' Thermostatistics
• Long-range interactions, doubling measures and Tsallis entropy
• Extensive limit of a non-extensive entanglement entropy

Cited by in corpus (3)

• Dimensionally regularized Tsallis' Statistical Mechanics and two-body Newton's gravitation
• Analysis of Tsallis' classical partition function's poles
• Hidden correlations entailed by q-non additivity render the q-monoatomic gas highly non trivial