Related papers: Riemannian thermo-statistics geometry
Thermodynamic fluctuation theory originated with Einstein who inverted the relation $S=k_B\ln\Omega$ to express the number of states in terms of entropy: $\Omega= \exp(S/k_B)$. The theory's Gaussian approximation is discussed in most…
Fluctuation geometry was recently proposed as a counterpart approach of Riemannian geometry of inference theory. This theory describes the geometric features of the statistical manifold $\mathcal{M}$ of random events that are described by a…
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…
I introduce a new geometrical approach to thermo--statistical mechanics. Here I highlight the main physical ideas, and how do they translate into geometrical language. I contrast the present approach with previous…
Starting from an axiomatic perspective, \emph{fluctuation geometry} is developed as a counterpart approach of inference geometry. This approach is inspired on the existence of a notable analogy between the general theorems of…
The fact that a temperature and an entropy may be associated with horizons in semi-classical general relativity has led many to suspect that spacetime has microstructure. If this is indeed the case then its description via Riemannian…
The black hole area theorem suggests that classical general relativity is the thermodynamic limit of a quantum statistics. The degrees of freedom of the statistical theory cannot be the spacetime metric. We argue that the statistical theory…
A generalized entropy arising in the context of superstatistics is obtained for an ideal gas. The curvature scalar associated to the thermodynamic space generated by this modified entropy is calculated using two formalisms of the geometric…
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…
Thermodynamics unavoidably contains fluctuation theory, expressible in terms of a unique thermodynamic information metric. This metric produces an invariant thermodynamic Riemannian curvature scalar $R$ which, in fluid and spin systems,…
A novel geometric formalism for statistical estimation is applied here to the canonical distribution of classical statistical mechanics. In this scheme thermodynamic states, or equivalently, statistical mechanical states, can be…
Going beyond the classical Gaussian approximation of Einstein's fluctuation theory, Ruppeiner gave it a Riemannian geometric structure with an entropic metric. This yielded a fundamental quantity - the Riemannian curvature, which was used…
A general investigation is made into the intrinsic Riemannian geometry for complex systems, from the perspective of statistical mechanics. The entropic formulation of statistical mechanics is the ingredient which enables a connection…
We study quantum statistical inference tasks of hypothesis testing and their canonical variations, in order to review relations between their corresponding figures of merit---measures of statistical distance---and demonstrate the crucial…
In this paper we consider the space of those probability distributions which maximize the $q$-R\'enyi entropy. These distributions have the same parameter space for every $q$, and in the $q=1$ case these are the normal distributions. Some…
The Boltzmann distribution of an ideal gas is determined by the Hamiltonian function generating single particle dynamics. Systems with higher complexity often exhibit topological constraints, which are independent of the Hamiltonian and may…
We present a review of the main aspects of geometrothermodynamics, an approach which allows us to associate a specific Riemannian structure to any classical thermodynamic system. In the space of equilibrium states, we consider a Legendre…
In the present work, we present a detailed discussion of a Riemannian metric structure originally introduced in [Gori et al., \textit{J. Stat. Mech.}, \textbf{9} 093204 (2018)] on the configuration space and on phase space allowing us to…
Understanding thermodynamics and statistical mechanics in the full general relativistic context is an open problem. I give tentative definitions of equilibrium state, mean values, mean geometry, entropy and temperature, which reduce to the…
A statistical model M is a family of probability distributions, characterised by a set of continuous parameters known as the parameter space. This possesses natural geometrical properties induced by the embedding of the family of…