FOUNDATIONS AND APPLICATIONS OF A MESOSCOPIC THERMODYNAMIC THEORY OF FAST PHENOMENA

A mesoscopic thermodynamic theory of fast phenomena is proposed. In pr inciple, such a description should include an infinite number of momen ts of the velocity distribution; in a frequency-wave-number space the corresponding transport coefficients would be expressed in terms of a continued fraction expansion. Our objective is to eliminate from the d escription a maximum number of fast variables. This is achieved by der iving an asymptotic expression of the continued fraction. This procedu re allows for a considerable reduction of the number of relevant varia bles, which are generally identified as the classical variables, such as energy and velocity, complemented by their corresponding dissipativ e fluxes, namely, the heat and the momentum fluxes. Two applications a re investigated: ultrasound propagation in dilute gases and heat trans port in dielectric crystals at very low temperature, where the phenome na of second sound is observed. It is shown that for ultrasound propag ation, the influence of the fast variables can be described by introdu cing so-called effective relaxation times. This results in better agre ement with experiments than earlier theoretical models and casts a lig ht on the foundation of mesoscopic formalisms, such as extended irreve rsible thermodynamics. Concerning heat conduction in dielectric crysta ls, it is seen that the present description includes the three differe nt modes of transport observed experimentally, namely, ballistic phono ns, second sound waves, and diffusion. Our approach is a generalizatio n of the models proposed by Cattaneo [Atti Sem. Univ. Modena 3, 33 (19 48)] and by Guyer and Krumhansl [Phys. Rev. 148, 766 (1966); 148, 778 (1966)].