Two-dimensional gravitating system in optimal Lagrange multiplier approach

We investigate a classical two-dimensional gravitating system in the context of Tsallis's statistical mechanics, using optimal Lagrange multiplier (OLM) approach. We obtain, in particular, an exact expression for equation of state of the system. To derive it we also employ the recent generalizations of thermodynamic quantities in Tsallis's formalism advanced by Abe et al. (Phys. Lett. A 281 (2001) 126) in order to adequately identify generalized free energy in our calculation and connect with generalized pressure. We show that our equation of state, in this approach, is independent of the nonextensive parameter q, and is equal to the ordinary result. (C) 2002 Elsevier Science B.V. All rights reserved.