Irreversibility as divergence from equilibrium

The entropy production is commonly used to gauge a system's distance from equilibrium, but this interpretation lacks formalization due to the absence of a natural equilibrium measure. This analysis shows that the entropy production of a Markov system measures its separation from specific equilibrium dynamics. These reference dynamics correspond to the closest reversible systems in the information-theoretic sense. This result yields new lower bounds for the entropy production and novel links between thermodynamics and information geometry.