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## A Mathematical Theory of the Supercritical State Serving as an Effective Means of Destruction of Chemical Warfare Agents

It is well known that the supercritical state of a gas has great dissolving capacity. In this paper, the mathematical reason for this phenomenon is studied in great detail.

The relationship between thermodynamics and economics has been known for a long time. The term ``thermoeconomics'' has even appeared. However, several aspects of the old thermodynamics are unacceptable in economics. For example, experts in thermodynamics believe that the diamond crystal is in the metastable state, and in due time will be transformed into graphite. However, these experts can hardly convince businessmen to part with their ancient diamonds.

The laws of economics require that the old conceptions of thermodynamicsa be mathematically scrutinized and reviewed.

The correspondence principle for quantum statistics, classical statistics and economics which associates the number of particles with the amount of money, the chemical potential with the nominal percentage, the negative pressure with debts, and the law of economic preference allowed to obtain agreement of the general theory of thermoeconomics with the latest experimental data.

Negative pressure also means negative energy and, therefore, “holes”, antiparticles. Continuation across infinity to negative energies is accomplished by using a parastatistical correction to the Bose-Einstein distribution.

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The surface-active substances everywhere are presented on the water surface, they are exposed to waves and currents, and are involved in the processes of ocean-atmosphere exchange. They play a prominent role in the formation of small-scale part of the spectrum of wind waves and affect the manifestations of internal waves on the sea surface. In this paper, on the basis of experimental data, measurements of the surface-active agents "in situ", calculated the probability distributions of elastic films of surface-active substances in the slicks (smoothed areas of the sea surface) for the two oceanic regions (the Pacific Ocean near the island of San Diego (California ) and the central part of the Atlantic Ocean between the equator and the 35th parallel of northern latitude and 1° - 65° W). Obtained almost the same distribution function of elasticity of the films of surface-active substances (in normalized variables), which indicates the existence of a universal "climatic" of the distribution function of elasticity of the films of surfactants. The results can be used to assess the visibility of slicks on the sea surface by remote radio-physical methods.

In the first part of the paper, we introduce the concept of observable quantities associated with a macroinstrument measuring the density and temperature and with a microinstrument determining the radius of a molecule and its free path length, and also the relationship between these observable quantities. The concept of the number of degrees of freedom, which relates the observable quantities listed above, is generalized to the case of low temperatures. An analogy between the creation and annihilation operators for pairs (dimers) and the creation and annihilation operators for particles (molecules) is carried out. A generalization of the concept of a Bose condensate is introduced for classical molecules as an analog of an ideal liquid (without attraction). The negative pressure in the liquid is treated as holes (of exciton type) in the density of the Bose condensate. The phase transition gas-liquid is calculated for an ideal gas (without attraction). A comparison with experimental data is carried out.

In the other part of the paper, we introduce the concept of new observable quantity, namely, of a pair (a dimer), as a result of attraction between the nearest neighbors. We treat in a new way the concepts of Boyle temperature T_B (as the temperature above which the dimers disappear) and of the critical temperature T_c (below which the trimers and clusters are formed). The equation for the Zeno line is interpreted as the relation describing the dependence of the temperature on the density at which the dimers disappear. We calculate the maximal density of the liquid and also the maximal density of the holes. The law of corresponding states is derived as a result of an observation by a macrodevice which cannot distinguish between molecules of distinct gases, and a comparison of theoretical and experimental data is carried out.

A model for organizing cargo transportation between two node stations connected by a railway line which contains a certain number of intermediate stations is considered. The movement of cargo is in one direction. Such a situation may occur, for example, if one of the node stations is located in a region which produce raw material for manufacturing industry located in another region, and there is another node station. The organization of freight traﬃc is performed by means of a number of technologies. These technologies determine the rules for taking on cargo at the initial node station, the rules of interaction between neighboring stations, as well as the rule of distribution of cargo to the ﬁnal node stations. The process of cargo transportation is followed by the set rule of control. For such a model, one must determine possible modes of cargo transportation and describe their properties. This model is described by a ﬁnite-dimensional system of diﬀerential equations with nonlocal linear restrictions. The class of the solution satisfying nonlocal linear restrictions is extremely narrow. It results in the need for the “correct” extension of solutions of a system of diﬀerential equations to a class of quasi-solutions having the distinctive feature of gaps in a countable number of points. It was possible numerically using the Runge–Kutta method of the fourth order to build these quasi-solutions and determine their rate of growth. Let us note that in the technical plan the main complexity consisted in obtaining quasi-solutions satisfying the nonlocal linear restrictions. Furthermore, we investigated the dependence of quasi-solutions and, in particular, sizes of gaps (jumps) of solutions on a number of parameters of the model characterizing a rule of control, technologies for transportation of cargo and intensity of giving of cargo on a node station.