Covariant formulation of the multidmeensional kinetic theory of phase transitions of the first kind

Conditions under which the thermodynamic and kinetic senses of instability and stability of the variables of state of a nucleating center are compatible are established. The existence and uniqueness of a transformation that determines the thermodynamically and kinetically unstable and stable variables are established. It is shown that these variables separate in the distribution of the nucleating centers and permit reduction of the multidimensional theory to a one-dimensional theory. A reduced description of the multidimensional phase space is constructed by means of a thermodynamically unstable variable. In the typical case of a symmetric and positive-definite matrix of diffusion coefficients of the kinetic equation a general solution of this equation is found.