  Energy efficiency is closely related to the evolution of biological systems
and is important to their information processing. In this paper, we calculated
the excitation probability of a simple model of a bistable biological unit in
response to pulsatile inputs, and its spontaneous excitation rate due to noise
perturbation. Then we analytically calculated the mutual information, energy
cost, and energy efficiency of an array of these bistable units. We found that
the optimal number of units could maximize this array's energy efficiency in
encoding pulse inputs, which depends on the fixed energy cost. We conclude that
demand for energy efficiency in biological systems may strongly influence the
size of these systems under the pressure of natural selection.
