Information geometry in vapour-liquid equilibrium

  title={Information geometry in vapour-liquid equilibrium},
  author={Dorje C. Brody and Daniel W. Hook},
  journal={arXiv: Statistical Mechanics},
Using the square-root map p-->\sqrt{p} a probability density function p can be represented as a point of the unit sphere S in the Hilbert space of square-integrable functions. If the density function depends smoothly on a set of parameters, the image of the map forms a Riemannian submanifold M in S. The metric on M induced by the ambient spherical geometry of S is the Fisher information matrix. Statistical properties of the system modelled by a parametric density function p can then be… Expand

Figures from this paper

Information geometry for the strongly degenerate ideal Bose–Einstein fluid
Abstract The thermodynamic geometry of the Bose–Einstein fluid in the framework of information geometry is revisited, and particularly the strongly degenerate case is considered for a finite volume.Expand
Information Geometry of Complex Hamiltonians and Exceptional Points
A general scheme for the geometric study of parameter-space manifolds of eigenstates of complex Hamiltonians is outlined here, leading to generic expressions for the metric. Expand
Riemannian geometry of fluctuation theory: An introduction
Fluctuation geometry was recently proposed as a counterpart approach of Riemannian geometry of inference theory (information geometry), which describes the geometric features of the statisticalExpand
Geometry of thermodynamic control.
This work constructs closed-form expressions for minimal-dissipation protocols for a particle diffusing in a one-dimensional harmonic potential and demonstrates that the friction tensor arises naturally from a first-order expansion in temporal derivatives of the control parameters, without appealing directly to linear response theory. Expand
Quantum lattice model with local multi-well potentials: Riemannian geometric interpretation for the phase transitions in ferroelectric crystals
Abstract Geometrical aspects of quantum lattice model with the local anharmonic potentials are presented for the case of deformed ferroelectric lattice. A metric is defined in a two-dimensional phaseExpand
Para-Sasakian geometry in thermodynamic fluctuation theory
In this work we tie concepts derived from statistical mechanics, information theory and contact Riemannian geometry within a single consistent formalism for thermodynamic fluctuation theory. WeExpand
Information geometry in quantum field theory: lessons from simple examples
Motivated by the increasing connections between information theory and high-energy physics, particularly in the context of the AdS/CFT correspondence, we explore the information geometry associatedExpand
Fluctuation geometry: a counterpart approach of inference geometry
Starting from an axiomatic perspective, fluctuation geometry is developed as a counterpart approach of inference geometry. This approach is inspired on the existence of a notable analogy between theExpand
Information geometry of density matrices and state estimation
Given a pure state vector |x and a density matrix , the function defines a probability density on the space of pure states parameterised by density matrices. The associated Fisher–Rao informationExpand
Jaynes' Maximum Entropy Principle, Riemannian Metrics and Generalised Least Action Bound
The set of solutions inferred by the generic maximum entropy (MaxEnt) or maximum relative entropy (MaxREnt) principles of Jaynes - considered as a function of the moment constraints or theirExpand


Statistical geometry in quantum mechanics
  • D. Brody, L. Hughston
  • Physics, Mathematics
  • Proceedings of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences
  • 1998
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 byExpand
Information geometry in functional spaces of classical and quantum finite statistical systems
Abstract Statistical states and bounded random variables (observables) of finite physical systems can be represented in real Banach spaces Ls1 and Ls∞, respectively. Since both norms are Krein-weak,Expand
Information geometry of the ising model on planar random graphs.
The solution in field of the Ising model is used on an ensemble of planar random graphs to evaluate the scaling behavior of the scalar curvature, and a plausible scaling relation is postulated: R approximately |beta-beta(c)|(alpha-2). Expand
Information geometry of finite Ising models
Abstract A model in statistical mechanics, characterised by a Gibbs measure, inherits a natural parameter-space geometry through an embedding into the space of square-integrable functions. ThisExpand
Riemannian geometry and stability of thermodynamical equilibrium systems
A geometrical approach to statistical thermodynamics is proposed. It is shown that any r-parameter generalised Gibbs distribution leads to a Riemannian metric of parameter space. The components ofExpand
Information geometry, one, two, three (and four)
Although the notion of entropy lies at the core of statistical mechanics, it is not often used in statistical mechanical models to characterize phase transitions, a role more usually played byExpand
Geometrization of statistical mechanics
  • D. Brody, L. Hughston
  • Mathematics
  • Proceedings of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences
  • 1999
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–spaceExpand
The Fisher-Rao Metric for Projective Transformations of the Line
  • S. Maybank
  • Mathematics, Computer Science
  • International Journal of Computer Vision
  • 2005
Experiments with the algorithm suggest that it can detect a projective transformation of the line even when the correspondences between the components of the measurements in the domain and the range of the projective Transformation are unknown. Expand
Geometrisation of Statistical Mechanics
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 spaceExpand
On the symmetry of real-space renormalisation
Abstract A geometric structure, arising from the embedding into a Hilbert space of the parametrised probability measure for a given lattice model, is applied here to study the symmetry properties ofExpand