The Hessian geometry of the ideal gas in rotation

Fuente: arXiv
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Main Author: de Maujouy, Jérémie Pierard
Format: Preprint
Published: 2024
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author de Maujouy, Jérémie Pierard
author_facet de Maujouy, Jérémie Pierard
contents We study the Hessian geometry associated with an ideal gas in a spherical centrifuge. According to Souriau, a spherically confined ideal gas admit states of thermal and rotational equilibrium. These states, called Gibbs states, form an exponential family with an action of the Euclidean rotation group. We investigate its Hessian (Fisher-Rao) geometry and show that in the high angular velocity limit, the geometry can be compared to the Hessian geometry of a spherical rigid body which we show to be isometric to a hyperbolic space.
format Preprint
id arxiv_https___arxiv_org_abs_2404_09035
institution arXiv
publishDate 2024
record_format arxiv
spellingShingle The Hessian geometry of the ideal gas in rotation
de Maujouy, Jérémie Pierard
Mathematical Physics
Differential Geometry
We study the Hessian geometry associated with an ideal gas in a spherical centrifuge. According to Souriau, a spherically confined ideal gas admit states of thermal and rotational equilibrium. These states, called Gibbs states, form an exponential family with an action of the Euclidean rotation group. We investigate its Hessian (Fisher-Rao) geometry and show that in the high angular velocity limit, the geometry can be compared to the Hessian geometry of a spherical rigid body which we show to be isometric to a hyperbolic space.
title The Hessian geometry of the ideal gas in rotation
topic Mathematical Physics
Differential Geometry
url https://arxiv.org/abs/2404.09035