Thermodynamic stability,critical points,and phase transitions in the theory of partial distribution functions

We consider the stability of the minimum of the thermodynamic potential treated as a functional of partial densities or correlation functions. We show that the loss of stability is related to critical points of thermodynamic functions. Curves or points of phase transitions of the first kind are determined by comparing the thermodynamic potentials of different phases, and the condition for loss of stability with respect to density fluctuations can be taken as the phase transition criterion only approximately. Phase transitions of the second kind are related to the loss of stability with respect to the pair correlation fluctuations. __________ Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 155, No. 3, pp. 512–523, June, 2008.     

Nonlocal approximations of the theory of the surface tension of a liquid

The first nonlocal term in the theory of the surface tension of a liquid is derived. The surface energy corresponding to this term is of the order of that corresponding to the local term. The resulting estimate of the surface tension agrees with the parachore rule.Translated from Izvestiya Vysschikh Uchebnykh Zavedenii, Fizika, No. 7, pp, 81–85, July, 1981.     

Multiparticle Direct Correlations

We study the properties of multiparticle direct correlations in detail and construct a system of successive approximations of the generating functional of direct correlation functions. Moreover, in contrast to the Bogoliubov–Born–Green–Kirkwood–Yvon hierarchy, this approach does not require approximating higher correlations. Our approximations determine the corresponding approximations of the thermodynamic potential. The irreducible parts of multiparticle direct correlations are constructed explicitly.     

The solid sphere model in studies of crystal stability

The possibility of employing the hard sphere model in studies of real, stable, inert-gas crystals is considered. On the basis of the firmly established phase transition criterion for a model system the stability curve of a real crystal is found, with attractive forces considered by first-order perturbation theory. The result obtained is compared with experiment.     

Statistical irreversibility and instability of motion according to Lyapunov

The stability of the motion of a system of many particles according to Lyapunov is discussed. It is shown that the set of initial displacements of the particles decomposes into sets which result in stable, and consequently mixed, motions. The mixing rate is characterized by the average statistical Lyapunov index, for which an expression is obtained in terms of the interaction potential and a function modulating the initial displacements of the particles. An integral equation is obtained for the latter.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 4, pp. 83–87, April, 1981.     

The temperature dependence of quantum distribution functions

In the present article we consider a method for obtaining the quantum distribution function in phase space given a specific choice of operator for a function of the coordinates and moments. The temperature equation is written for this function. We obtain the operator expression for the temperature quantum distribution function in phase space.In conclusion the authors would like to express their thanks to V. A. Kuchin for valuable observations in discussing the study.