Cosh gradient systems and tilting

We review a class of gradient systems with dissipation potentials hyperbolic-cosine type. show how such emerge in large deviations jump processes, multi-scale limits diffusion and more. the exponential nature cosh derives from scaling arises implicitly cell problems limits. discuss in-depth role "tilting" systems. Certain classes are "tilt-independent", which means that changing driving functional does not lead to changes potential. Such tilt-independence separates potential, guarantees clear modelling interpretation, gives rise strong notions gradient-system convergence. although general many tilt-independent, certain cosh-type not. also this is inevitable, by studying detail classical example Kramers high-activation-energy limit, converges process Wasserstein system system. explain pre-limit lost limit This same lack independence can be recognized theories chemical reaction rates chemical-engineering literature. illustrate similar discrete setting. For "two-terminal" fast subnetworks, we give complete characterization dependence on tilting, strongly resembles theory equivalent electrical networks.