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.

翻译：我们提出一种分子动力学中计算输运系数的方法。输运系数量化了受小外力驱动的非平衡系统中通量的线性依赖性。标准的非平衡方法固定外力并测量系统被驱动至非平衡状态时产生的平均通量，而一种相反的策略是固定通量值并测量诱发该通量所需外力的平均大小。这种方法的确定性版本称为诺顿动力学，由Evans和Morris在20世纪80年代研究。在本工作中，我们引入该方法的随机版本，首先为一大类扩散过程建立通用形式理论，随后将其专门化至常用于分子动力学模拟的欠阻尼朗之万动力学。我们提供数值证据表明，随机诺顿方法能等效地测量线性响应，并且实际上证明这种等效性远远超出线性响应区域。本研究从理论和数值两个角度提出了许多引人深思的问题。