Analysis of Tsallis' classical partition function's poles

Abstract

When one integrates the q-exponential function of Tsallis' so as to get the partition function $Z$, a gamma function inevitably emerges. Consequently, poles arise. We investigate here here the thermodynamic significance of these poles in the case of $n$ classical harmonic oscillators (HO). Given that this is an exceedingly well known system, any new feature that may arise can safely be attributed to the poles' effect. We appeal to the mathematical tools used in [EPJB 89, 150 (2016) and arXiv:1702.03535 (2017)], and obtain both bound and unbound states. In the first case, we are then faced with a classical Einstein crystal. We also detect what might be interpreted as pseudo gravitational effects.

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References in corpus (7)

• Lynden-Bell and Tsallis distributions for the HMF model
• 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
• Tsallis thermostatics as a statistical physics of random chains
• Extensive limit of a non-extensive entanglement entropy
• Hidden correlations entailed by q-non additivity render the q-monoatomic gas highly non trivial
• Strong correlations between the exponent $\alpha$ and the particle number for a Renyi-monoatomic gas in Gibbs' statistical mechanics

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