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Article

Violation of Carath\'eodory axioms at the critical point of a gas. Frenkel point as a critical point of the transition ``liquid-amorphous solid'' in the region of negative pressure

Mathematical notes. 2014. Vol. 96. No. 6. P. 977-982.

 We give a geometric interpretation of the thermodynamic potential,  free and internal energy, and enthalpy in terms of a Lagrangian manifold in the phase space of pairs (T, -S), (-mu, N), and (P,V) of intensive and extensive variables.
 The Lagrangian manifold is viewed as the dequantization of the tunnel canonical operator.  With this approach, the critical point is a point where the equilibrium quasi-static process described by the Carath\'eodory axioms is violated.  For a hard liquid with negative pressure, we present a model of a multi-modulus medium.