Geometrothermodynamics of interface domain structures in phase transitions on 5-dimensional contact statistical manifold with pseudo-Finsler metric

Abstract

Geometrothermodynamics of interface domains emerging in rst-order phase transitions modeled on a 5-dimensional statistical contact manifold is proposed in entropy representation. The supporting structure is given by a space-time regarded a hypersurface embedded in the tangent space, and its signature is provided by the Hessian of a pseudo-Finsler- type Lagrangian. A many-relaxation-time evolution of domains (nuclei) is represented a set of sections of the indicatrix surface in the tangent space at di erent pseudo-times. Within the phase-transition space-time, whose Finsler-metric signature is (􀀀 􀀀 􀀀), we say that such a section - obtained from sectioning the indicatrix by a plane transversal to pseudo- time axis - lives in the physically meaningful region of the space-time, and its geodesics are associated with a stable state of the domain structure. If the indicatrix section evolves from the physically meaningful region into a region with alternating-sign metric signature, this testi es that the domain structure associated with the geodesic loses its stability and becomes a metastable one.