A path-dependent entropic Lagrangian formulation for exact thermoviscous evolution of sheared magnetic tori with anisotropic resistivity
Abstract
Resistive evolution of a three-dimensional magnetostatic equilibrium requires compatibility among induction, momentum balance and thermal transport. We construct exact thermoviscous evolutions of a non-axisymmetric magnetic torus with nonzero magnetic shear using a path-dependent entropic Lagrangian (PDEL) formulation. A symmetric positive-definite resistivity tensor is constructed so that the resistive differential expression preserves the spatial form of a known sheared toroidal equilibrium. Homogeneous expansion is coupled to an ideal gas and positive bulk viscosity in the absence of body forces and volumetric heat supply. For a one-temperature gas with heat-capacity ratio 5/3, a T−2/3 resistivity prefactor gives elementary time dependence for all fields. A two-temperature extension admits a Te−3/2 prefactor and positive interspecies heat exchange on a finite state interval. Material magnetic flux decays while the rotational-transform profile is preserved. Both branches satisfy local total-energy conservation, moving-boundary power balance and material transport of dissipation histories. A seed-specific obstruction excludes positive scalar resistivity along the same homologous trajectory; the two-temperature exchange law has a nonremovable endpoint pole. Symbolic identities, independent Cartesian differentiation and surface--volume quadrature verify these results. The solutions provide coupled MHD benchmarks with passive, inverse-designe
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BibTeX
@misc{ren2026pathdependent,
title = {{A path-dependent entropic Lagrangian formulation for exact thermoviscous evolution of sheared magnetic tori with anisotropic resistivity}},
author = {Huilong Ren},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.37305},
eprint = {2610.37305},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.37305},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - A path-dependent entropic Lagrangian formulation for exact thermoviscous evolution of sheared magnetic tori with anisotropic resistivity
AU - Huilong Ren
PY - 2026
DA - 2026/10/27
PB - arXiv
DO - 10.48550/arxiv.2610.37305
UR - https://arxiv.org/abs/2610.37305
AB - Resistive evolution of a three-dimensional magnetostatic equilibrium requires compatibility among induction, momentum balance and thermal transport. We construct exact thermoviscous evolutions of a non-axisymmetric magnetic torus with nonzero magnetic shear using a path-dependent entropic Lagrangian (PDEL) formulation. A symmetric positive-definite resistivity tensor is constructed so that the resistive differential expression preserves the spatial form of a known sheared toroidal equilibrium. Homogeneous expansion is coupled to an ideal gas and positive bulk viscosity in the absence of body forces and volumetric heat supply. For a one-temperature gas with heat-capacity ratio 5/3, a T^−2/3 resistivity prefactor gives elementary time dependence for all fields. A two-temperature extension admits a T_e^−3/2 prefactor and positive interspecies heat exchange on a finite state interval. Material magnetic flux decays while the rotational-transform profile is preserved. Both branches satisfy local total-energy conservation, moving-boundary power balance and material transport of dissipation histories. A seed-specific obstruction excludes positive scalar resistivity along the same homologous trajectory; the two-temperature exchange law has a nonremovable endpoint pole. Symbolic identities, independent Cartesian differentiation and surface--volume quadrature verify these results. The solutions provide coupled MHD benchmarks with passive, inverse-designe
ER -