Recent unfoldings on Mutual Linearity

Título: Recent unfoldings on Mutual Linearity Resumo: Standard response theory, from linear response to Onsager reciprocity, only holds for small perturbations. This seminar is about what happens when a control is pushed to arbitrary strength instead. Fix one control in a nonequilibrium system (a single rate, force, or reaction constant), and any individual observable traces a nonlinear curve as that control varies. But any two such observables turn out to be rigidly tied together: they are confined to the same one-dimensional response, and plotting one against the other reveals an exact straight line, with no small-perturbation assumption, arbitrarily far from equilibrium. I will survey how far this rigidity reaches. From its original discrete-state formulation for states and currents, through continuous Langevin dynamics and chemical reaction networks, to a Laplace-domain version that governs the full relaxation transient. Together, they suggest that nonequilibrium response is far more constrained than expected, a hint that a universal theory of genuinely nonequilibrium response may be within reach.