On the multidimensional theory of the first-order phase transitions

Multidimensional theory of first-order phase transitions in the vicinity of a one-dimensional saddle point is considered. Transformations of the variables describing new-phase nuclei are suggested; these transformations allow one to completely separate the variables in the Fokker-Planck equation and reduce the problem to a one-dimensional one. The distribution function and the nucleation rate are found for both stationary and non-stationary nucleation stages. As an illustration, the problem of boiling of a volatile liquid is considered in the case where new-phase nuclei are characterized by two parameters.