  Reaction Coordinates (RCs) are indicators of hidden, low-dimensional
mechanisms that govern the long-term behavior of high-dimensional stochastic
processes. We present a novel and general variational characterization of
optimal RCs and provide conditions for their existence. Optimal RCs are
minimizers of a certain loss function and reduced models based on them
guarantee very good approximation of the long-term dynamics of the original
high-dimensional process. We show that, for slow-fast systems, metastable
systems, and other systems with known good RCs, the novel theory reproduces
previous insight. Remarkably, the numerical effort required to evaluate the
loss function scales only with the complexity of the underlying,
low-dimensional mechanism, and not with that of the full system. The theory
provided lays the foundation for an efficient and data-sparse computation of
RCs via modern machine learning techniques.
