Extended structural dynamics of charged media: kinetic theory, generalized plasma dynamics, and structural temperature splitting

This paper extends the Extended Structural Dynamics (ESD) framework, in which particles possess finite spatial extent and internal degrees of freedom (rotation, orientation, deformation) coupled to translational motion, to charged media. Previous work established entropy growth mechanisms and non-Fourier transport behavior for neutral structured particles [P. BarAvi, “Extended structural dynamics: Emergent irreversibility from reversible dynamics.” arXiv:2505.09650 [physics.class-ph], 2025, P. BarAvi, “Structural viscosity, thermal waves, and the Mpemba effect from extended structural dynamics,” arXiv:2603.02249 [physics.class-ph], 2026]; here we incorporate electromagnetic interactions. Starting from a minimally coupled ESD–electromagnetic Hamiltonian, we derive an extended Boltzmann–Vlasov equation in which electromagnetic torque terms enter explicitly in the streaming operator, a feature absent from point-particle kinetic theories. A Chapman–Enskog expansion with BGK closure yields a generalized Maxwell–Navier–Stokes system including structural stress, an orientation dynamics equation, and modified energy and transport relations. Transport coefficients are expressed in terms of structural parameters and relaxation times within the adopted closure. A central result is a structural temperature splitting in magnetized systems, <m:math xmlns:m="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <m:mfrac> <m:mrow> <m:msub> <m:mrow> <m:mi>T</m:mi> </m:mrow> <m:mrow> <m:mtext>trans</m:mtext> </m:mrow> </m:msub> </m:mrow> <m:mrow> <m:msub> <m:mrow> <m:mi>T</m:mi> </m:mrow> <m:mrow> <m:mtext>rot</m:mtext> </m:mrow> </m:msub> </m:mrow> </m:mfrac> <m:mo>=</m:mo> <m:mn>1</m:mn> <m:mo>+</m:mo> <m:msup> <m:mrow> <m:mfenced close=")" open="("> <m:mrow> <m:msub> <m:mrow> <m:mi>τ</m:mi> </m:mrow> <m:mrow> <m:mtext>rot</m:mtext> </m:mrow> </m:msub> <m:msub> <m:mrow> <m:mi>ω</m:mi> </m:mrow> <m:mrow> <m:mi>c</m:mi> </m:mrow> </m:msub> </m:mrow> </m:mfenced> </m:mrow> <m:mrow> <m:mn>2</m:mn> </m:mrow> </m:msup> </m:math> TₜᵣₐₙₛTᵣₒₜ=1+(τ ᵣₒₜω c)² , where ω c = qB / m . For parameters relevant to complex plasma experiments (e.g., PK-4), the scaling yields order-of-magnitude consistency with observed temperature anisotropies. The results suggest that structural degrees of freedom can contribute to transport and non-equilibrium behavior in charged media.