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In the region of negative pressures P, the addend γ corresponding to the number of degrees of freedom D = 2 γ + 2 is less than zero. The energy equal to E = V P is also less than zero. Therefore, it is natural to introduce a negative relative temperature as the mean energy. The negative pressure on the negative spinodal tends to minus infinity as T → 0. Accordingly, the negative relative temperature will also approach minus infinity. As the chemical potential μ→−∞, μ/ T → 0, the asymptotic behavior of the thermodynamic quantities gives rise to amebas of special form in tropical (idempotent) analysis. It is shown that the theoretical isotherms obtained in this paper coincide with the isotherms of van derWaals gas up to the third decimal place. For theoretical distributions, transitions to amorphic solids (glass) occurs. [ABSTRACT FROM AUTHOR]

The notion of ideal liquid for the number of degrees of freedom less than 2, i.e., γ < 0, is introduced. The values of the pressure P and of the compressibility factor Z on the spinodal in the negative pressure region for the van der Waals equation determine the value of γ, γ( T) < 0, for μ = 0. For $$T \leqslant \frac{{{3^3}}}{{{2^5}}}{T_c}$$, a relationship with the van der Waals equation is established. [ABSTRACT FROM AUTHOR]

The article offers information on the concept of old thermodynamics and new thermodynamics and mentions the differences between them. Topics discussed include concerns of old thermodynamics with the gas-liquid phase transition, concerns of new thermodynamics on metastable states and explanation given by physicists on metastability of live human beings.

We construct gas and liquid binodals assuming that both the gas and the liquid branch of the spinodal are given. To determine how the number of degrees of freedom depends on temperature, we use the main formula expressing the compressibility factor via the ratio of two Riemann functions. The behavior of the second virial coefficient is studied for a given spinodal, which serves as an analog of caustics. The gas- and liquid-amorphous solid transitions are considered on the second sheet. An argument in favor of the mapping of the second sheet onto the negative quadrant {- P,- Z} is presented. [ABSTRACT FROM AUTHOR]