2025/10/28 by Ateşli, Begüm, Esen, Oğul, Grmela, Miroslav +1 · 1 citation
#FOS: Physical sciences #Mathematical Physics (math-ph)
paper · doi:10.48550/arxiv.2510.24300
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.