Gamma-convergence of a gradient-flow structure to a non-gradient-flow structure

Abstract We study the asymptotic behaviour of a gradient system in regime which driving energy becomes singular. For this gradient-system convergence concepts are ineffective. characterize limiting different way, by proving $$\Gamma $$ Γ -convergence so-called energy-dissipation functional , combines components and dissipation single functional. The -limit these functionals again characterizes variational evolution, but limit is not any system. question describes diffusion particle one-dimensional double-well landscape, small noise. wells have depth, small-noise process converges to Markov on two-state system, jumps only happen from higher lower well. This transmutation into evolution non-gradient type model for how many one-directional chemical reactions emerge as reversible ones. proved paper both identifies ‘fate’ structure irreversible reactions.