We wrote kinetic equation for the *average* *x* as

(6) |

We can speak only about *average* properties of *f*(*t*). We will
calculate and . We will average over
*equilibrium* ensemble.

Averaging (6), we obtain:

or(7) |

(8) |

But we know ! Result:

This could be rewritten as This is possible only if for But and depends only on . We obtain: From symmetry Since is(9) |

(10) |

Sometimes the function *f*(*t*) is called *random noise.*
Equation (9) shows that random noise is
-correlated. In other words, all harmonics are present in its
Fourier transform with equal weights
(equation (10)). Such noise is called
*white noise* (remember rainbow?).

*Colored noise:* not all harmonics are equal^{}:

How can it be so? What's wrong in our derivation?

(11) |

Another interpretation: the -function in equation (9) is the -function only approximately. In fact it is a sharp peak with the width about the characteristic time of the molecular processes.

© 1997

Tue Oct 28 22:16:24 EST 1997