Analysis of Tsallis’ classical partition function’s poles

A. Plastino and M.C. Rocca

Physica A: Statistical Mechanics and its Applications, 2017, vol. 487, issue C, 196-204

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 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 Plastino et al. (2016) and Plastino and Rocca (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.

Keywords: q-Statistics; Divergences; Partition function; Dimensional regularization; Specific heat (search for similar items in EconPapers)
Date: 2017
References: View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:487:y:2017:i:c:p:196-204

DOI: 10.1016/j.physa.2017.06.026

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