The Magnusian generator for dissipative systems and application to leading 2.5PN radiation-reaction dynamics
Abstract
The Magnusian is a phase-space function that generates finite-time evolution through nested Poisson brackets. It is related to several familiar generators of classical dynamics, including the radial action, the eikonal phase and related quantities. In this work, we extend the Magnusian framework to systems with dissipation and nonlocal-in-time interactions using the in-in formalism, also known as the Schwinger-Keldysh or Galley formalism. This framework is particularly natural for binary dynamics, where integrating out the mediating gravitational field can produce both dissipative radiation-reaction effects and hereditary, nonlocal-in-time interactions. We derive the generalized Magnusian and show that it continues to generate finite-time evolution. As an application, we construct the Magnusian for Newtonian bound motion subject to the leading 2.5PN radiation-reaction force. The resulting generator defines a discrete evolution map from one cycle to the next and describes the evolution of the system in agreement with numerical solutions.
Versions
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BibTeX
@misc{blanco2026magnusian,
title = {{The Magnusian generator for dissipative systems and application to leading 2.5PN radiation-reaction dynamics}},
author = {Francisco M. Blanco},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2607.24335},
eprint = {2607.24335},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2607.24335},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - The Magnusian generator for dissipative systems and application to leading 2.5PN radiation-reaction dynamics
AU - Francisco M. Blanco
PY - 2026
DA - 2026/09/01
PB - arXiv
DO - 10.48550/arxiv.2607.24335
UR - https://arxiv.org/abs/2607.24335
AB - The Magnusian is a phase-space function that generates finite-time evolution through nested Poisson brackets. It is related to several familiar generators of classical dynamics, including the radial action, the eikonal phase and related quantities. In this work, we extend the Magnusian framework to systems with dissipation and nonlocal-in-time interactions using the in-in formalism, also known as the Schwinger-Keldysh or Galley formalism. This framework is particularly natural for binary dynamics, where integrating out the mediating gravitational field can produce both dissipative radiation-reaction effects and hereditary, nonlocal-in-time interactions. We derive the generalized Magnusian and show that it continues to generate finite-time evolution. As an application, we construct the Magnusian for Newtonian bound motion subject to the leading 2.5PN radiation-reaction force. The resulting generator defines a discrete evolution map from one cycle to the next and describes the evolution of the system in agreement with numerical solutions.
ER -