Sensory capacity: an information theoretical measure of the performance of a sensor

TL;DR

This paper introduces the concept of sensory capacity as an information-theoretic measure of sensor performance, demonstrating how memory enhances capacity and revealing a tradeoff between capacity and efficiency within a thermodynamic framework.

Contribution

It defines sensory capacity for stochastic sensors, analyzes the impact of memory, and establishes a fundamental tradeoff with efficiency using stochastic thermodynamics.

Findings

Adding memory increases sensory capacity.

Maximum capacity (1) limits efficiency to below 1/2.

Explicit analytical results for a cellular network sensor model.

Abstract

For a general sensory system following an external stochastic signal, we introduce the sensory capacity. This quantity characterizes the performance of a sensor: sensory capacity is maximal if the instantaneous state of the sensor has as much information about a signal as the whole time-series of the sensor. We show that adding a memory to the sensor increases the sensory capacity. This increase quantifies the improvement of the sensor with the addition of the memory. Our results are obtained with the framework of stochastic thermodynamics of bipartite systems, which allows for the definition of an efficiency that relates the rate with which the sensor learns about the signal with the energy dissipated by the sensor, which is given by the thermodynamic entropy production. We demonstrate a general tradeoff between sensory capacity and efficiency: if the sensory capacity is equal to its maximum 1, then the efficiency must be less than 1/2. As a physical realization of a sensor we consider a two component cellular network estimating a fluctuating external ligand concentration as signal. This model leads to coupled linear Langevin equations that allow us to obtain explicit analytical results.