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：我们提出了一种在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离平衡时诱导的平均通量，而另一种互补的途径是固定通量值，并测量诱导该通量所需外力的平均大小。这种方法的一个确定性版本，称为诺顿动力学，在20世纪80年代由埃文斯和莫里斯研究。在本工作中，我们引入了该方法的随机版本，首先为一大类扩散过程发展了一般形式理论，然后将其特化为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，随机诺顿方法提供了线性响应的等价度量，并且实际上证明这种等价性远超出线性响应区域。这项工作从理论和数值角度都提出了许多引人深思的问题。