Asymmetry of fluctuation with respect to time reversal in steady states of biological systems.

The asymmetry of fluctuation with respect to time reversal which is expected in an energy-consuming steady state is discussed with special attention to biological systems. The necessary condition for asymmetry of fluctuation of an observed quantity is given. To show the usefulness of the experimental analysis of asymmetry of fluctuation, some calculations are carried out on two simple examples of three-state reactions. In one of them, the two-point time correlation function of the observed quantity has an oscillatory component, while in the other the function is nearly exponential, but in both cases, the fluctuation has a pronounced asymmetry. A method to estimate the degree of asymmetry of fluctuation is proposed, and the application of the present method to investigation of the molecular events in biological systems such as muscle is discussed.