Thermodynamical irreversible approach for the stellar pulsation problem

In this paper, the stellar pulsation theory is reformulated following an ir reversible thermodynamic approach (Lavenda, Thermodynamics of Irreversible Processes, Deliver, New York, 1993). A general stability criterion and a th ermodynamic Langrangian for the Pulsating star problem are obtained using a variational method (Sicardi and Ferro Fontan, Phys. Lett. 113A (1958) 263; Sicardi et at., J. Math. Phys. 32 (1991) 1350). This formulation, based on the calculation of a free energy excess function, is applied to the adiaba tic, non-adiabatic, radial and non-radial cases and, as a result, the alrea dy known energy principles arc obtained as particular cases of the general stability criterion mentioned above. Eigenvectors and eigenvalues can be ca lculated in a systematic way from the thermodynamic Lagrangian obtained for the general dissipative case (being independent of the adiabatic one). Thi s allows a better determination of periods and oscillation frequencies. (C) 2001 Published by Elsevier Science B.V.