Abstract
This paper presents a preliminary analysis of the system behavior that works far from the thermodynamical equilibrium states in the environment with limited resources. The examples of such systems are the real computer systems. Nowadays in such systems the runoff characteristic of the information flow is very turbulent in contradiction to the current existing laminar models. These systems work under constant overload, which means a permanent thermodynamical non-equilibrium (from the thermodynamical point of view). For such a situation the classical approach to their modeling is still based on Boltzmann-Gibbs (BG) thermodynamics,which is proper only for systems that are in equilibriumstate (sometimes called thermostatic) or very close to it. The changing number of tasks N in such systems and the limited resourcesK of the environment cause its chaotic behavior and generate the dependencies that have got a long-termproperty. Such processes degrade the system performance X and elongate the response time R; in other words degrade the Quality of Service (QoS). To understand the whole behavior of such systems one needs a proper thermodynamical basis that seems to be the Tsallis formula of the non-extensive entropy.