Contact Large Deviations of Stochastic Vector Bundles
Abstract
Large deviation theory lacks a geometric foundation for its rate functions and fluctuation symmetries. This paper develops a contact large deviation theory on stochastic vector bundles, in which the rate function, the scaled cumulant generating function, and a Gallavotti--Cohen-type fluctuation duality all follow from the contact 1-form. The constraint function acts as a generalized Lagrangian; the least constraint principle yields the dynamics, and the contact potential is built order by order from the master equation, producing a coupled Hamilton--Jacobi--transport system governed by the invariant density, drift, and fluctuation tensor. The contact path measure satisfies a large deviation principle with rate function given by the constraint action; the scaled cumulant generating function obeys a stationary eigenvalue equation with a Donsker--Varadhan variational characterization. The entropy production rate, the fluctuation--dissipation combination e=1/2 gT Ag−σ, is the physical observable; the time-reversal involution J:(t,y,ϕ)↦(t,y,−ϕ−∇lnρ) with reversed drift vrev=−v+Ag yields a Gallavotti--Cohen-type duality λfwd(q)=λrev(q+1)+λfwd(−1). The classical one-dimensional GC symmetry is recovered in the reversible case Ag=0.
Related
- Large Deviations in Stochastic Dynamics: A Hamiltonian Perspective
- Uniform Large Deviations, Barrier Identity and the Néel--Arrhenius Law for the One-Dimensional Stochastic Landau--Lifshitz--Gilbert Equation
- Polynomial stability conditions for vector bundles: positivity, equivariance and blow-ups
- Stable atomic vector bundles are 1-obstructed
- Tangent bundles of Quot schemes of vector bundles on curves
BibTeX
@misc{zhong2026contact,
title = {{Contact Large Deviations of Stochastic Vector Bundles}},
author = {D. Y. Zhong},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.19679},
eprint = {2609.19679},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.19679},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Contact Large Deviations of Stochastic Vector Bundles
AU - D. Y. Zhong
PY - 2026
DA - 2026/09/17
PB - arXiv
DO - 10.48550/arxiv.2609.19679
UR - https://arxiv.org/abs/2609.19679
AB - Large deviation theory lacks a geometric foundation for its rate functions and fluctuation symmetries. This paper develops a contact large deviation theory on stochastic vector bundles, in which the rate function, the scaled cumulant generating function, and a Gallavotti--Cohen-type fluctuation duality all follow from the contact 1-form. The constraint function acts as a generalized Lagrangian; the least constraint principle yields the dynamics, and the contact potential is built order by order from the master equation, producing a coupled Hamilton--Jacobi--transport system governed by the invariant density, drift, and fluctuation tensor. The contact path measure satisfies a large deviation principle with rate function given by the constraint action; the scaled cumulant generating function obeys a stationary eigenvalue equation with a Donsker--Varadhan variational characterization. The entropy production rate, the fluctuation--dissipation combination e=1/2 g^T Ag−σ, is the physical observable; the time-reversal involution J:(t,y,ϕ)↦(t,y,−ϕ−∇lnρ) with reversed drift v^rev=−v+Ag yields a Gallavotti--Cohen-type duality λ_fwd(q)=λ_rev(q+1)+λ_fwd(−1). The classical one-dimensional GC symmetry is recovered in the reversible case Ag=0.
ER -