This paper discusses the evaluation of hydrodynamic variables in the presence of
spontaneous fluctuations, such as in molecular simulations of fluid flows. The
principal point is that hydrodynamic variables such as fluid velocity and temperature
must be defined in terms of mechanical variables such as momentum and energy
density). Because these relations are nonlinear and because fluctuations of
mechanical variables are correlated, care must be taken to avoid introducing a bias
when evaluating means, variances, and correlations of hydrodynamic variables. The
unbiased estimates are formulated; some alternative, incorrect approaches are
presented as cautionary warnings. The expressions are verified by numerical
simulations, both at thermodynamic equilibrium and at a nonequilibrium steady
state.
