Dynamic stability versus thermodynamic performance in a simple model for a Brownian motor.

Homeostasis allows living organisms to perform in optimal conditions despite ever-changing surroundings. Dynamically, it corresponds to a stable steady state, and so its quality can be judged by the volume of the corresponding basin of attraction and/or the length of the relaxation time. Motivated by the fact that the vast majority of intracellular processes involve enzymatic reactions and, as some people have suggested, models similar to those of Brownian motors can be used to study them, here we introduce a simple Brownian motor model and use it to gain insight into the relation between efficiency and stability properties previously observed in macroscopic systems. For this, we analyze the existence, uniqueness, and stability of the motor's steady state; study its thermodynamic process variables, their relation, and their dependence on the model parameters; and compare the Brownian motor relaxation time and thermodynamic properties. Finally, since the steady state is unique and globally stable, we discuss our results from the standpoint of the energetic costs of maintaining a homeostatic state with short relaxation times.