Thermodynamical irreversible approach for the stellar pulsation problem

In this paper, the stellar pulsation theory is reformulated following an irreversible thermodynamic approach (Lavenda, Thermodynamics of Irreversible Processes, Denver, New York, 1993). A general stability criterion and a thermodynamic Langrangian for the pulsating star problem are obtained using a variational method (Sicardi and Ferro Fontán, Phys. Lett. 113A (1958) 263; Sicardi et al., J. Math. Phys. 32 (1991) 1350). This formulation, based on the calculation of a free energy excess function, is applied to the adiabatic, non-adiabatic, radial and non-radial cases and, as a result, the already known energy principles are obtained as particular cases of the general stability criterion mentioned above. Eigenvectors and eigenvalues can be calculated in a systematic way from the thermodynamic Lagrangian obtained for the general dissipative case (being independent of the adiabatic one). This allows a better determination of periods and oscillation frequencies.