  Maximum entropy principle identifies forces conjugated to observables and the
thermodynamic relations between them, independent upon their underlying
mechanistic details. For data about state distributions or transition
statistics, the principle can be derived from limit theorems of infinite data
sampling. This derivation reveals its empirical origin and clarify the meaning
of applying it to large but finite data. We derive an uncertainty principle for
the statistical variations of the observables and the inferred forces. We use a
toy model for molecular motor as an example.
