S.Sh. Rekhviashvili, D.Sh. Gavashili
In article the model is presented where the fractal dimension D is parameter filling of a solid phonon gas. This fractal dimension, as well as the corresponding phonon structure of solids, it is logical to call the spectral.
Using the expression for an elementary fractal volume per one allowed state and the formula for calculating the fractal medium in the wavenumber space, calculated the number of modes. Next, we derive a formula for the density of states for the characteristic frequency.
The quantum-statistical method is used for calculation of thermal conductivity coefficient subject to into account the Bose-Einstein distribution for phonons. It is show that the generalization of the theory to the case of fractal media does not change the basic form of expression for the thermal conductivity corresponding to the kinetic theory of gases. We consider some new aspects of the thermodynamics of fractals. Noted that the fractal dimension can serve as an intensive thermodynamic parameter when states of incomplete thermodynamic equilibrium of the system (by analogy with the order parameter in the theory of phase transitions)