Unbounded Probability Theory and Its Applications

Маслов, В. П.; Maslova, T. V.

doi:10.1137/s0040585x97986084

Cited by 5 publications

(2 citation statements)

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“…Note also that, due to absence of attraction, an ideal liquid is completely plastic; namely, it does not try to return to the original state (the state before stretching). In this sense, the Bose condensate for γ < 0, which leads to this "kind" of liquid, can also be treated more visually as a glass or an amorphous solid 5 . This makes it possible to interpret the state of the liquid for γ < 0 more intuitively.…”

Section: Holes In the Bose Condensate As Observable Quantitiesmentioning

confidence: 99%

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Thermodynamics as a multistep relaxation process and the role of observables in different scales of quantities

Maslov¹

2013

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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. In this paper, the observations in three scales, macro, micro, and nano, are studied.

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Section: Holes In the Bose Condensate As Observable Quantitiesmentioning

confidence: 99%

“…where nj stands for the average number of particles in each of the G i states of the jth group and α and β are some constants (see [2], the footnote on p. 184, and also [4] and [5]), the entropy must be of the form…”

Section: Introductionmentioning

confidence: 99%