  We present a method to compute transport coefficients in molecular dynamics.
Transport coefficients quantify the linear dependencies of fluxes in
non-equilibrium systems subject to small external forcings. Whereas standard
non-equilibrium approaches fix the forcing and measure the average flux induced
in the system driven out of equilibrium, a dual philosophy consists in fixing
the value of the flux, and measuring the average magnitude of the forcing
needed to induce it. A deterministic version of this approach, named Norton
dynamics, was studied in the 1980s by Evans and Morris. In this work, we
introduce a stochastic version of this method, first developing a general
formal theory for a broad class of diffusion processes, and then specializing
it to underdamped Langevin dynamics, which are commonly used for molecular
dynamics simulations. We provide numerical evidence that the stochastic Norton
method provides an equivalent measure of the linear response, and in fact
demonstrate that this equivalence extends well beyond the linear response
regime. This work raises many intriguing questions, both from the theoretical
and the numerical perspectives.
