Parameter Lagrange coefficients

The idea is to construct a Lagrange function which has the same energy as the non-variational wave function, but which is variational in all parameters. Consider for example a CL wave function, which is variational in the state coefficients (a) but not in the MO coefficients (c) (note that we employ lower case c for the MO coefficients, but capital C to denote all wave function parameters, i.e. C contains both a and c), since they are determined by the stationary condition for the HF wave function. 

The idea is to construct a Lagrange function which has the same energy as the non-variational wave function, but which is variational in all parameters. Consider for example a CL wave function, which is variational in the state coefficients (a) but not in... 

The application of direct variational method for solution of Euler-Lagrange equation is similar to that in Sect. 3.2.2.1. It ailows to obtain the free energy in the form of polarization power series with the coefficients dependent on average particles radius and the parameters of Euler-Lagrange equation (3.45). In particular, surface polarization Pd in the boundary conditions leads to appearance of built-in field Ecyi(R), which can be written as... 

The Boltzmann integro-differential kinetic equation written in terms of statistical physics became the foundation for construction of the structure of physical kinetics that included derivation of equations for transfer of matter, energy and charges, and determination of kinetic coefficients that entered into them, i.e. the coefficients of viscosity, heat conductivity, diffusion, electric conductivity, etc. Though the interpretations of physical kinetics as description of non-equilibrium processes of relaxation towards the state of equilibrium are widespread, the Boltzmann interpretations of the probability and entropy notions as functions of state allow us to consider physical kinetics as a theory of equilibrium trajectories. These trajectories as well as the trajectories of Euler-Lagrange have the properties of extremality (any infinitesimal part of a trajectory has this property) and representability in the form of a continuous sequence of states of rest. These trajectories can be used to describe the behavior of (a) isolated systems that spontaneously proceed to final equilibrium (b) the systems for which the differences of potentials with the environment are fixed (c) and non-homogeneous systems in which different parts have different values of the same intensive parameters. 

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