2002/11/30 by Atsushi Taruya, Masa-aki Sakagami, Masa‐aki Sakagami · 2 citations
Physics and Astronomy · #Advanced Thermodynamics and Statistical Mechanics #Quantum Mechanics and Non-Hermitian Physics #Statistical Mechanics and Entropy #astro-ph #cond-mat.stat-mech #gr-qc #hep-ph
paper · pdf · doi:10.1016/s0378-4371(03)00039-6
published as Physica A322 (2003) 285-312 · 35 pages, 6 figures, accepted for publication in Physica A (2003)
arxiv created 2003/01/05 · openalex publication_date 2003/04/25 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We revisit the issues on the thermodynamic property of stellar self-gravitating system arising from Tsallis' non-extensive entropy. Previous papers (Taruya & Sakagami, Physica A 307 (2002) 185 (cond-mat/0107494); ibid. (2002) in press (cond-mat/0204315)) have revealed that the extremum-state of Tsallis entropy characterized by the so-called stellar polytrope has consistent thermodynamic structure, which predicts the thermodynamic instability due to the negative specific 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 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 confined 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 specific heat and within the formalism, the stellar polytrope is characterized as a plausible non-extensive meta-equilibrium state.