The problem mentioned in the title is studied.
Рассчитан термодинамический потенциал сверхпроводящего квантового цилиндра. Изучена зависимость критической температуры и теплоемкости сверхпроводящей системы от концентрации электронов и радиуса нанотрубки.
We consider the relations between thermodynamics on the one hand and the (max,+)-algebra and tropical mathematics on the other hand. The contribution of Grigorii Litvinov to tropical geometry is emphasized. Relations for a liquid in the negative pressure domain are given.
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.