Abstract: In this talk, I introduce two complementary approaches to study the thermodynamics of horizons perturbatively away from stationarity in arbitrary diffeomorphism-invariant theories of gravity with non-minimal matter couplings. (1) Light-ray focusing: on the dynamical horizon, we prove a generalised focusing theorem encoding horizon thermodynamics: under positive null energy flux, light rays converge when their expansion is measured by the Wall entropy density rather than the area element. Wall entropy extends Bekenstein–Hawking and Wald entropies and satisfies the first and second laws. With higher-spin fields, the theorem and laws persist subject to a “higher-spin focusing condition”, proposed as a consistency constraint. (2) Symmetry: near-stationary horizons possess a perturbatively broken boost symmetry whose improved Noether charge defines the Hollands–Wald–Zhang dynamical entropy, which offers another dynamical generalisation of Wald entropy. We extend this from pure gravity to general theories with arbitrary bosonic matter couplings, analyse horizon temperature variations, and treat charged black objects—strings, rings, and branes, etc.—with p-form charges in one framework, deriving the associated first and second laws. Finally, the two approaches unify: the event-horizon dynamical entropy equals the Wall entropy of the generalised apparent horizon.