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.
After revision:  We prove exactly that, when the receptor system does not perturb the signal dynamics is not perturbed by the receptors, lower bounded by the product of the mutual informationand the time-scale of signal dynamics.