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.Comment: 15 pages, 7 figure
