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 (condmat/0204315)) have revealed that the extremum-state of Tsallis entropy characterized by the so-called stellar polytrope has consistent thermodynamic structur...