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Geometry of hypersurfaces defined by the relation which generalizes classical formula for free energy in terms of microstates is studied. Induced metric, Riemann curvature tensor, Gauss-Kronecker curvature and associated entropy are calculated. Special class of ideal statistical hypersurfaces is analyzed in details. Non-ideal hypersurfaces and their singularities similar to those of the phase transitions are considered. Tropical limit of statistical hypersurfaces and double scaling tropical limit are discussed too.
Tropical limit for macroscopic systems in equilibrium defined as the formal limit of Boltzmann constant k going to 0 is discussed. It is shown that such tropical limit is well-adapted to analyse properties of systems with highly degenerated energy le
Statistical physics has proven to be a very fruitful framework to describe phenomena outside the realm of traditional physics. The last years have witnessed the attempt by physicists to study collective phenomena emerging from the interactions of ind
We present a unified formulation for quantum statistical physics based on the representation of the density matrix as a functional integral. We identify the stochastic variable of the effective statistical theory that we derive as a boundary configur
The image of physics is connected with simple mechanical deterministic events: that an apple always falls down, that force equals mass times acceleleration. Indeed, applications of such concept to social or historical problems go back two centuries (
In this work we study a simple compartmental model for drinking behavior evolution. The population is divided in 3 compartments regarding their alcohol consumption, namely Susceptible individuals $S$ (nonconsumers), Moderate drinkers $M$ and Risk dri