Related papers: On the physical significance of geometrothermodyna…
In the variational approach to statistical mechanics, equilibrium states are the rigorous analogues of thermodynamic phases; the question of which invariant measures can arise as equilibrium states is therefore the question of which phases…
We first apply functional-integral approach to a multiband Hubbard model near the critical pairing temperature, and derive a generic effective action that is quartic in the fluctuations of the pairing order parameter. Then we consider…
The geometry of thermodynamic state space is studied for asymptotically anti-de Sitter black holes in D-dimensional space times. Convexity of thermodynamic potentials and the analytic structure of the response functions is analysed. The…
We discuss here the use of generalized forms of entropy, taken as information measures, to characterize phase transitions and critical behavior in thermodynamic systems. Our study is based on geometric considerations pertaining to the space…
A possible way to capture the effects of quantum gravity in spacetime at a mesoscopic scale, for relatively low energies, is through an energy dependent metric, such that particles with different energies probe different spacetimes. In this…
Classical and quantum statistical mechanics are cast here in the language of projective geometry to provide a unified geometrical framework for statistical physics. After reviewing the Hilbert space formulation of classical statistical…
For more than half a century, moments have attracted lot ot interest in the pattern recognition community.The moments of a distribution (an object) provide several of its characteristics as center of gravity, orientation, disparity, volume.…
We consider 2d QFTs as relevant deformations of CFTs in the thermodynamic limit. Using causality and KPZ universality, we place a lower bound on the timescale characterizing the onset of hydrodynamics. The bound is determined parametrically…
We study classical limit for quantum mechanics with two times and temperature, which describes a generalized dynamics of relativistic point mass. In this theory, thermodynamic time means a parameter of evolution, whereas geometric time is…
This work assembles some basic theoretical elements on thermal equilibrium, stability conditions, and fluctuation theory in self-gravitating systems illustrated with a few examples. Thermodynamics deals with states that have settled down…
Generalized dimensions of multifractal measures are usually seen as static objects, related to the scaling properties of suitable partition functions, or moments of measures of cells. When these measures are invariant for the flow of a…
A paradigm based on the absolute equilibrium of Galerkin-truncated inviscid systems to aid in understanding turbulence [T.-D. Lee, "On some statistical properties of hydrodynamical and magnetohydrodynamical fields," Q. Appl. Math. 10, 69…
In these notes we review some properties of Statistical Quantum Field Theory at equilibrium, i.e Quantum Field Theory at finite temperature. We explain the relation between finite temperature quantum field theory in (d,1) dimensions and…
We study phase transitions in the thermodynamic description of Pomeau-Manneville intermittent maps from the point of view of infinite ergodic theory, which deals with diverging measure dynamical systems. For such systems, we use a…
Motivated by the notion that the mathematics of gravity can be reproduced from a statistical requirement of maximal entropy, we study the consequence of introducing an entropic source term in the Einstein-Hilbert action. For a spatially…
The analysis of phase transitions in cosmological spacetimes shows that their existence requires a time-dependent apparent horizon radius, which in turn implies an equation of state different from that of a dark energy fluid. This condition…
The generalized Gibbs free energy and enthalpy is derived in the framework of nonextensive thermodynamics by using the so-called physical temperature and the physical pressure. Some thermodynamical relations are studied by considering the…
We investigate the influence of diffraction on the statistics of energy levels in quantum systems with a chaotic classical limit. By applying the geometrical theory of diffraction we show that diffraction on singularities of the potential…
In this paper, the generalized second law (GSL) of thermodynamics and entropy is revisited in the context of cosmological models in Gauss-Bonnet gravity with the boundary of the universe is assumed to be enclosed by the dynamical apparent…
The sine-Gordon model is a paradigmatic quantum field theory that provides the low-energy effective description of many gapped 1D systems. Despite this fact, its complete thermodynamic description in all its regimes has been lacking. Here…