In molecular dynamics, transport coefficients measure the sensitivity of the invariant probability measure of the stochastic dynamics at hand with respect to some perturbation. They are typically computed using either the linear response of nonequilibrium dynamics, or the Green--Kubo formula. The estimators for both approaches have large variances, which motivates the study of variance reduction techniques for computing transport coefficients. We present an alternative approach, called the \emph{transient subtraction technique} (inspired by early work by Ciccotti and Jaccucci in 1975), which amounts to simulating a transient dynamics, from which we subtract a sensibly coupled equilibrium trajectory, resulting in an estimator with smaller variance. We present the mathematical formulation of the transient subtraction technique, give error estimates on the bias and variance of the associated estimator, and demonstrate the relevance of the method through numerical illustrations for various systems.

翻译：在分子动力学中，输运系数衡量了所研究随机动力学的不变概率测度对某种扰动的敏感性。通常采用非平衡动力学的线性响应或Green-Kubo公式进行计算。这两种方法的估计量都具有较大方差，这促使我们研究用于计算输运系数的方差缩减技术。我们提出了一种称为瞬态减法技术的新方法（灵感源自Ciccotti与Jaccucci于1975年的早期工作），该方法通过模拟瞬态动力学，并从中减去经过合理耦合的平衡轨迹，从而获得方差更小的估计量。我们给出了瞬态减法技术的数学表述，对其估计量的偏差和方差进行了误差估计，并通过多种系统的数值算例验证了该方法的适用性。