Gibbs Manifolds
Optimization and Control
2022-11-29 v1 Mathematical Physics
Algebraic Geometry
math.MP
Quantum Physics
Abstract
Gibbs manifolds are images of affine spaces of symmetric matrices under the exponential map. They arise in applications such as optimization, statistics and quantum~physics, where they extend the ubiquitous role of toric geometry. The Gibbs variety is the zero locus of all polynomials that vanish on the Gibbs manifold. We compute these polynomials and show that the Gibbs variety is low-dimensional. Our theory is applied to a wide range of scenarios, including matrix pencils and quantum optimal transport.
Cite
@article{arxiv.2211.15490,
title = {Gibbs Manifolds},
author = {Dmitrii Pavlov and Bernd Sturmfels and Simon Telen},
journal= {arXiv preprint arXiv:2211.15490},
year = {2022}
}
Comments
22 pages