The cross correlation properties of composite systems.

A new method is presented for characterizing cross correlations in composite systems described by a couple of time-dependent random variables. This method is based on (i) rescaling the time derivatives of the variables to make their variances unity and then (ii) recombining these rescaled variables into their sum and difference. This manipulation enables one to express the joint probability distribution function in a peculiar way. It is also found that the entropy of composite systems is not equal to the sum of entropy of each subsystem because of the cross correlations.