Thermodynamic limits to information harvesting by sensory systems

In view of the relation between information and thermodynamics we investigate how much information about an external protocol can be stored in the memory of a stochastic measurement device given an energy budget. We consider a layered device with a memory component storing information about the external environment by monitoring the history of a sensory part coupled to the environment. We derive an integral fluctuation theorem for the entropy production and a measure of the information accumulated in the memory device. Its most immediate consequence is that the amount of information is bounded by the average thermodynamic entropy produced by the process. At equilibrium no entropy is produced and therefore the memory device does not add any information about the environment to the sensory component. Consequently, if the system operates at equilibrium the addition of a memory component is superfluous. Such device can be used to model the sensing process of a cell measuring the external concentration of a chemical compound and encoding the measurement in the amount of phosphorylated cytoplasmic proteins.