Before revision:  We show that this limit arises from a fundamental trade-off between the removal of the extrinsic noise in the receptor state and the suppression of the intrinsic noise in the signaling network. We next prove that only non-equilibrium systems can lift this trade-off : They can integrate the receptor state over time while suppressing the intrinsic noise by using energy to store the receptor state into stable modification states of the readout molecules.
After revision:  We show that this limit arises from a fundamental trade-off between the removal of the extrinsic noise in the receptor state and the suppression of the intrinsic noise in the downstream network. Non-equilibrium systems can lift this trade-off : They can integrate the receptor state over time while suppressing the intrinsic noise by using energy to store the receptor state into stable modification states of the readout molecules.