Abstract
A phase transition of the first kind is a jump of a function, a phase transition of the second kind is a jump of its first derivative, a phase transition of the third kind, a jump of the second derivative. A phase transition from one statistic to another is very gradual, but finally it is as considerable as the phase transition of the first kind. However, we cannot introduce a clearly defined parameter to which this transition corresponds. This is due to the fact that the fluctuations near the critical point are huge, and this violates, in the vicinity of that point, the main law of equilibrium thermodynamics, which asserts that fluctuations are relatively small.
The paper describes the transition in the supercritical fluid region of equilibrium thermodynamics from parastatistics to mixed statistics, in which the Boltzmann statistics is realized for long-living clusters. In economics this corresponds to a negative nominal credit rate. Examples of this non-standard situation are presented.
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Maslov, V.P., Maslova, T.V. Parastatistics and phase transition from a cluster as a fluctuation to a cluster as a distinguishable object. Russ. J. Math. Phys. 20, 468–475 (2013). https://doi.org/10.1134/S1061920813040080
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DOI: https://doi.org/10.1134/S1061920813040080