Reaction coordinates are indicators of hidden, low-dimensional mechanisms that govern
the long-term behavior of high-dimensional stochastic systems. We present a novel, very
general characterization of these coordinates and provide conditions for their existence. We
show that these conditions are ful�lled for slow-fast systems, metastable systems, and other
systems with known good reaction coordinates. Further, we formulate these conditions as
a variational principle, i.e., de�ne a loss function whose minimizers are optimal reaction
coordinates. Remarkably, the numerical e�ort 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. In summary, we provide the theoretical foundation for an e�cient computation
of reaction coordinates via modern machine learning techniques
