Before revision:  Here, we employ Koopman operator theory and ideas from dynamic mode decomposition (DMD) to show how TICA /VAC can be used to estimate the unbiased equilibrium distribution from short-trajectory data and further this result in order to construct unbiased estimators for expectations, covariance matrices, TICA/VAC eigenvectors, relaxation timescales , and reaction coordinates .
After revision:  Here, we employ Koopman operator theory and ideas from dynamic mode decomposition (DMD) to extend the VA and TICA to non-equilibrium data. The main insight is that the VA and TICA provide a coefficient matrix that we call Koopman model, as it approximates the underlying dynamical (Koopman) operator in conjunction with the basis set used. This Koopman model can be used to estimate the unbiased equilibrium distribution from short-trajectory data and further this result in order to construct unbiased estimators for expectations, covariance matrices, TICA/VAC eigenvectors, relaxation timescales , and reaction coordinates .