  In this paper we extend the parametric sensitivity analysis (SA) methodology
proposed in Ref. [Y. Pantazis and M. A. Katsoulakis, J. Chem. Phys. 138, 054115
(2013)] to continuous time and continuous space Markov processes represented by
stochastic differential equations and, particularly, stochastic molecular
dynamics as described by the Langevin equation. The utilized SA method is based
on the computation of the information-theoretic (and thermodynamic) quantity of
relative entropy rate (RER) and the associated Fisher information matrix (FIM)
between path distributions. A major advantage of the pathwise SA method is that
both RER and pathwise FIM depend only on averages of the force field therefore
they are tractable and computable as ergodic averages from a single run of the
molecular dynamics simulation both in equilibrium and in non-equilibrium steady
state regimes. We validate the performance of the extended SA method to two
different molecular stochastic systems, a standard Lennard-Jones fluid and an
all-atom methane liquid and compare the obtained parameter sensitivities with
parameter sensitivities on three popular and well-studied observable functions,
namely, the radial distribution function, the mean squared displacement and the
pressure. Results show that the RER-based sensitivities are highly correlated
with the observable-based sensitivities.
