Geometric Dissipation Structures and the Koszul Form
Abstract
This paper investigates the canonical Koszul one-form at the interface of Jean Marie Souriau's Lie group thermodynamics and Paulette Libermann's symplectically complete foliations to describe geometric dissipation. On the Poincaré half-plane ℍ under SL(2, ℝ), the equivariant momentum map level sets form a regular Libermann foliation framing the conservative boundaries. The Koszul-derived dissipative vector field acts strictly transverse to these leaves, driving a metriplectic flow that breaks Noether conservation laws and generates entropy. Quantum wise, we develop Berezin quantization on para-Kähler symmetric spaces, where the Koszul potential acts as a weight determining state density via the Fisher Souriau metric, and formalize Kostant's geometric quantization using the real dual polarizations of a bi-Lagrangian web.
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BibTeX
@misc{assandje2026geometric,
title = {{Geometric Dissipation Structures and the Koszul Form}},
author = {Prosper Rosaire Mama Assandje and Frédéric Barbaresco and Romain Nimpa Pefoukeu and Michel Bertrand Djiadeu Ngaha and Nozah Mba Frankel},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.30976},
eprint = {2609.30976},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.30976},
note = {CC0},
}
RIS
TY - UNPB
TI - Geometric Dissipation Structures and the Koszul Form
AU - Prosper Rosaire Mama Assandje
AU - Frédéric Barbaresco
AU - Romain Nimpa Pefoukeu
AU - Michel Bertrand Djiadeu Ngaha
AU - Nozah Mba Frankel
PY - 2026
DA - 2026/09/25
PB - arXiv
DO - 10.48550/arxiv.2609.30976
UR - https://arxiv.org/abs/2609.30976
AB - This paper investigates the canonical Koszul one-form at the interface of Jean Marie Souriau's Lie group thermodynamics and Paulette Libermann's symplectically complete foliations to describe geometric dissipation. On the Poincaré half-plane ℍ under SL(2, ℝ), the equivariant momentum map level sets form a regular Libermann foliation framing the conservative boundaries. The Koszul-derived dissipative vector field acts strictly transverse to these leaves, driving a metriplectic flow that breaks Noether conservation laws and generates entropy. Quantum wise, we develop Berezin quantization on para-Kähler symmetric spaces, where the Koszul potential acts as a weight determining state density via the Fisher Souriau metric, and formalize Kostant's geometric quantization using the real dual polarizations of a bi-Lagrangian web.
ER -