# Information geometry in vapour-liquid equilibrium

@article{Brody2008InformationGI, title={Information geometry in vapour-liquid equilibrium}, author={Dorje C. Brody and Daniel W. Hook}, journal={arXiv: Statistical Mechanics}, year={2008} }

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

#### 51 Citations

Information geometry for the strongly degenerate ideal Bose–Einstein fluid

- Physics
- 2021

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

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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

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Geometry of thermodynamic control.

- Physics, Medicine
- Physical review. E, Statistical, nonlinear, and soft matter physics
- 2012

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

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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 phase… Expand

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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. We… Expand

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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 associated… Expand

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- Mathematics, Physics
- 2012

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 the… Expand

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- Physics, Mathematics
- 2011

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 information… Expand

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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 their… Expand

#### References

SHOWING 1-10 OF 94 REFERENCES

Statistical geometry in quantum mechanics

- 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 by… Expand

Information geometry in functional spaces of classical and quantum finite statistical systems

- Mathematics
- 1981

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.

- Mathematics, Medicine
- Physical review. E, Statistical, nonlinear, and soft matter physics
- 2002

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

- Mathematics
- 2003

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. This… Expand

Riemannian geometry and stability of thermodynamical equilibrium systems

- Mathematics
- 1990

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 of… Expand

Information geometry, one, two, three (and four)

- Physics
- 2003

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 by… Expand

Geometrization of statistical mechanics

- 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–space… Expand

The Fisher-Rao Metric for Projective Transformations of the Line

- 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

- Physics
- 1997

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… Expand

On the symmetry of real-space renormalisation

- Physics
- 1998

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 of… Expand