The Onsager-Machlup action as a consciousness measure: uniqueness, comparison, and reinterpretation

The Onsager-Machlup (OM) action — the Lagrangian of stochastic dynamics — appears through- out computational neuroscience as a tool for computing transition rates and formulating dynamical principles, but has never been employed as a quantitative index of the cognitive state. We survey these applications and identify the gap they leave: no existing work evaluates the kinetic compo- nent of the OM action along realized trajectories as a state measure. We then show, drawing on uniqueness theorems from information geometry and path-space maximum entropy, that this kinetic component — Ω = κR gij(vi −fi)(vj −fj)dt — is the unique consciousness-related quantity com- patible with the structure of causal statistical manifolds. We compare Ω systematically with the entropy production rate, fluctuation-dissipation theorem violation metrics, and Schro ̈dinger bridge transition costs, proving that these measures evaluate different vector fields in the same Fisher met- ric and decouple in physically realizable limits. Reinterpreting existing OM-based results through the lens of Ω, we derive the temperature-independence of perceptual switching rates and show that the free energy principle emerges as the saddle-point limit of the full path integral.