Using Monte Carlo simulations to predict the distribution of properties in an ensemble of fluctuating ratchets

We demonstrate the use of Metropolis Monte Carlo simulations and a two-state fluctuating ratchet model to predict the distribution of microscopic properties in a sample of Brownian motors. Our scheme only uses the information about the mean and standard deviation of steady-state velocities of motors. We interpret the results using an analogy between the ensemble of motors and the semi grand canonical ensemble used to study mixtures of chemical species. We observe that increasing the proportion of motors having faster transitions between two states will always increase the mean velocity of the sample, irrespective of the extent of variation in other microscopic properties. On the other hand, changing the proportion of motors based on their potential energies in a particular state has a noticeable effect on mean velocity only when the sample is made homogeneous with respect to most other microscopic properties. The computational approach is easily extendable to models beyond fluctuating ratchets and observables beyond steady-state velocities.