BROWNIAN SYSTEM PRESENTATION

Bohdan Lev (Personal webpage)

According to basic principles of thermodynamics, when a macroscopicsystem is brought into contact with a thermal bath, the systemevolves in time approaching the equilibrium state in the course ofrelaxation. The state of equilibrium is well defined only undercertain idealized conditions, so that the properties of such systemare determined by its peculiarities and characteristics of thethermal bath. In most cases, however, the systems are subjected tonon-equilibrium conditions and external constraints. Therefore, itis difficult, if not impossible, to determine the governingparameters that can be held constant.

Nevertheless, there exist stationary states that can beunambiguously defined for certain open systems. Examples of suchsystems are given by hot electrons in semiconductors, a system ofphotons on inhomogeneous scatterers, when the difraction coeficientdepends on the frequency of photons, a system of high-energyparticles in accelerators that originates from collision withmacroscopic particles in dusty plasma. Currently, there does notexist a well-developed description method of the nonequilibriumdistribution function, which would take into account possible systemstates. A standard method describing non-equilibrium states is basedon the information on the equilibrium state and small deviationsfrom this state. The nonequilibrium in this approach is treated as asmall modification of the equilibrium distribution function.Although far-from-equilibrium systems are abundant in nature, thereis no unified commonly accepted theoretical approach whichdetermines possible states of such systems.

Hence, it is a fundamentally important task to develop a method forexploring general properties of stationary states of open systemsand to establish conditions of their existence. The main idea ofthis presentation consists in the description of the evolution of anon-equilibrium system as a possible Brownian motion of the systembetween different states with dissipation energy and diffusion inthe energy space. For brevity, such systems will be referred to asBrownian systems. It should be emphasized that the theory of theBrownian motion can be applied to the non-equilibrium systems too.The main goal is to present a simple way to describe thenon-equilibrium systems in the energy space and to obtain a newspecial solution. A few nonlinear models of systems with differentprocesses will be described.