Geometric Foundation of Nonequilibrium Transport: A Minkowski Embedding of Markov Dynamics

Abstract: We introduce a unified framework for analyzing Markov dynamics by linking nonequilibrium thermodynamics with information geometry. Using the symmetrized Kullback-Leibler divergence, we reveal an intrinsic Minkowski structure in the parameter space that naturally separates symmetric elements, governed by kinetic activities and forces, from the antisymmetric behavior, characterized by thermodynamic currents and affinities. This formulation offers a systematic approach to probe the transport properties of Markov systems.