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arXiv · 2510.24300

On Geometry of Dissipation in Multiscale Dynamics and Thermodynamics

Begüm Ateşli·Oğul Esen·Miroslav Grmela·Michal Pavelka
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Abstract

This manuscript introduces novel approaches to three phenomena. First, we extend the algebraic formulation of kinetic theory within the contact framework by making explicit the gauge freedom, thereby obtaining a formulation in which the phase-space volume itself becomes an additional dynamical variable. Second, we develop a new and simpler geometric formulation of the GENERIC framework, unifying Hamiltonian and gradient dynamics in a contact-geometric setting. This is realized within a specifically constructed graph space, which naturally emerges as an intermediate structure in the geometric Hamilton-Jacobi framework. Finally, we formulate a geometric extension of non-equilibrium thermodynamics in the setting of geometric Hamilton-Jacobi theory, allowing for the inclusion of microturbulence - a key feature of complex dynamical systems.

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Begüm Ateşli, Oğul Esen, Miroslav Grmela, Michal Pavelka. 2025-10-28. On Geometry of Dissipation in Multiscale Dynamics and Thermodynamics. https://arxiv.org/abs/2510.24300

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