Emergent Spinorial Structure in Mesoscopic Irreversible Thermodynamics

Abstract

We reconstruct a geometry of thermodynamic coordinates from transport coefficients within a mesoscopic canonical model. Self-adjoint flux observables determine a compatible evolution generator containing symmetric and antisymmetric transport coefficients. When the Hermitian transport tensor is positive, an exact graded first-order factorization reproduces this generator on its scalar sector. Its commutators define a spectral distance whose metric depends only on the symmetric tensor. Gradients of the antisymmetric tensor can change the evolution while leaving the metric unchanged. The construction allows coordinate-dependent coefficients. In the constant Onsager regime, a Clifford representation gives the same distance and an algebra fixed by the transport matrix. Published transport data for a $\mathrm{Bi_2Te_3}$ film give a principal-distance ratio of approximately $2.12$ in normalized coordinates at $ZT\simeq0.68$. We also examine a separate quadratic entropy-production observable and distinguish its discrete spectrum from the spectrum of the evolution generator. The spinorial representation adds no physical spin degrees of freedom.