Gravothermal catastrophe and Tsallis’ generalized entropy of self-gravitating systems. (III). Quasi-equilibrium structure using normalized q-values
✍ Scribed by Atsushi Taruya; Masa-aki Sakagami
- Publisher
- Elsevier Science
- Year
- 2003
- Tongue
- English
- Weight
- 422 KB
- Volume
- 322
- Category
- Article
- ISSN
- 0378-4371
No coin nor oath required. For personal study only.
✦ Synopsis
We revisit the issues on the thermodynamic property of stellar self-gravitating system arising from Tsallis' non-extensive entropy. Previous papers (Physica A 307 (2002) 185; ibid. 318 (2003) 387) have revealed that the extremum-state of Tsallis entropy, the so-called stellar polytrope, has consistent thermodynamic structure, which predicts the thermodynamic instability due to the negative speciÿc heat. However, their analyses heavily relies on the old Tsallis formalism using standard linear mean values. In this paper, extending our previous study, we focus on the quasi-equilibrium structure based on the standard framework by means of the normalized q-expectation values. It then turns out that the new extremum-state of Tsallis entropy essentially remains unchanged from the previous result, i.e., the stellar quasi-equilibrium distribution can be described by the stellar polytrope. While the thermodynamic stability for a system conÿned in an adiabatic wall completely agrees with the previous study and thereby the stability/instability criterion remains unchanged, the stability analysis reveals a new equilibrium property for the system surrounded by a thermal bath. In any case, the stability/instability criteria are consistently explained from the presence of negative speciÿc heat and within the formalism, the stellar polytrope is characterized as a plausible non-extensive meta-equilibrium state.