Before revision:  We prove exactly that, when the receptor system does not perturb the signal dynamics , the free energy consumed by the measurement process is lower bounded by the product of the mutual informationand the time-scale of signal dynamics. Our results apply to arbitrary network topologies and transition rates , and therefore should hold as a general principle for biomolecular information processing .
After revision:  We prove exactly that, when the receptor system does not perturb the signal dynamics , the free energy consumed by the measurement process is lower bounded by a quantity proportional to the mutual information. Our result is completely independent of the receptor architecture and dependent on signal properties alone , and therefore should hold as a general principle for biomolecular information processing .