The Second Law from Quantum Information: Information Geometry, Thermodynamics, and Gravity

"We derive the second law of thermodynamics from two fundamental information-theoretic ingredients: (A1) the monotonicity of relative entropy under CPTP maps, and (EFP) the existence of an equilibrium fixed point. We prove these conditions are both necessary and sufficient for non-negative entropy production. The paper establishes a rigorous three-step mathematical theorem: information monotonicity forces a C^2 potential S_{rel}, which in turn forces Helmholtz integrability, uniquely leading to the Lovelock class of gravitational dynamics. This framework bridges the gap between quantum information geometry and the Einstein equations of state."