Transport Determines Spectral Distance in Mesoscopic Thermodynamics

We derive a distance between thermodynamic states from a positive Hermitian transport tensor within a mesoscopic canonical model. An exact first-order factorization of the evolution generator gives a commutator norm and the metric G=2g-1, where g denotes the symmetric transport tensor. Gradients of the antisymmetric tensor can change the evolution, but they leave this distance unchanged. The construction allows coordinate-dependent coefficients. For constant Onsager coefficients, a Clifford representation gives the same metric. In a two-channel thermoelectric system, the ratio of normalized principal distances is sqrt 1+ZT + sqrt ZT. Transport coupling thus fixes the anisotropy of this metric. The construction requires neither an independent metric nor a physical spin variable.