Thermodynamic stability of continuous body (Q1068574)

\textit{M. E. Gurtin} [Arch. Rat. Mech. Anal. 59, 63-96 (1975; Zbl 0341.73003)], has been proposed a general stability theory of thermodynamics. In this paper the author extends Gurtin's stability theory to the non-autonomous case. A slightly modified version of Gurtin's theory of dynamical systems is presented, and some new sufficient conditions for Lyapunov stability of thermodynamical systems are proved. The paper is a real contribution towards bringing about a unified general theory of dynamical systems and a general stability theory of thermodynamics.