Thermodynamic uncertainty relation for biomolecular processes

Biomolecular systems like molecular motors or pumps, transcription and translation machinery, and other enzymatic reactions can be described as Markov processes on a suitable network. We show quite generally that in a steady state the dispersion of observables like the number of consumed/produced molecules or the number of steps of a motor is constrained by the thermodynamic cost of generating it. An uncertainty $ϵ$ requires at least a cost of $2k_{B}T\mathrm{/}{ϵ}^2$ independent of the time required to generate the output.