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arXiv · 2511.09375

A $k$-contact Geometrical Approach to Pseudo-Gauge Transformation

Mykhailo Hontarenko·Javier de Lucas·Adam Maskalaniec
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Abstract

We propose a starting point to the geometric description for the pseudo-gauge ambiguity in relativistic hydrodynamics, showing that it corresponds to the freedom to redefine the thermodynamic equilibrium state of the system. To do this, we develop for the first time a description of a relativistic hydrodynamic-like theory using $k$-contact geometry. In this approach, thermodynamic laws are encoded in a $k$-contact form, thermodynamical states are described via $k$-contact Legendrian submanifolds, and conservation laws emerge as a consequence of Hamilton-de Donder-Weyl (HdDW) equations. The inherent non-uniqueness of these solutions is identified as the source of the pseudo-gauge freedom. We explicitly demonstrate how this redefinition of equilibrium works in a model of a Bjorken-like expansion, where a pseudo-gauge transformation is shown to leave the physical dissipation invariant.

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Mykhailo Hontarenko, Javier de Lucas, Adam Maskalaniec. 2025-11-12. A $k$-contact Geometrical Approach to Pseudo-Gauge Transformation. https://arxiv.org/abs/2511.09375

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