Collective energy dissipation and fluctuations in elastoplastic systems

Starting from the equations of motion of a simple system possessing the properties of elastic and plastic bodies, we reconstruct its Lagrangian and Hamiltonian functions and also the so-called Rayleigh dissipation function. This allows us to find the rate of the system 'heating' and to analyze the fluctuations of the basic observables. In this way a rather general scheme of solving analogous problems in more complex elastoplastic systems is established. The paper gives a basis for studying open problems in the nuclear fusion and heavy-ions quasi-elastic collisions processes. It may be applied also for the theoretical treatment of dynamical problems in the other mesoscopic systems of fermions