  In the study of gravitational waves (GWs), the stochastic background
generated by compact binary systems are among the most important kinds of
signals. The reason for such an importance has to do with their probable
detection by the interferometric detectors [such as the Advanced LIGO (ALIGO)
and Einstein Telescope (ET)] in the near future. In this paper we are concerned
with, in particular, the stochastic background of GWs generated by double
neutron star (DNS) systems in circular orbits during their periodic and
quasi--periodic phases. Our aim here is to describe a new method to calculate
such spectra, which is based on an analogy with a problem of Statistical
Mechanics. Besides, an important characteristic of our method is to consider
the time evolution of the orbital parameters.
