Stability of complex systems and technogenic risk

Abstract

Mankind has become intensively engaged in studying the biotic mechanisms of the planet because of the increase in the number of new technologies that have pronounced but not always successfully predicted social, medicobiological, and ecological consequences. It has become necessary to associate any action that affects the environment with a forecast of its possible results. This assumes that in each specific problem area there exist ideas concerning the investigated processes, estimates of the significance of different solutions, and assumptions concerning alternatives and different development possibilities. Human experience, stimulated by a marked deterioration in the living environment, has already raised the question of determining the limits of homeostasis, i.e., of the critical environmental parameter values beyond which the existence of civilization, as presently understood, turns out to be impossible. However, it is now also evident that society will not be ready in the foreseeable future to relate in comparable terms the dangers of differing technical solutions to the kinds of activities needed to achieve the optimal relationship between social benefit and possible damage. It is therefore timely to devise some universal concept to describe the influence of the artificial living environment on the conditions for existence that will enable it to be extended to all types of technogenic activity. This essentially means that it is necessary to establish the interrelationship between the stability of complex systems and technogenic risk.Since the evolution of an artificial living environment involves the processes of transmitting matter, energy, and information, thermodynamic concepts can be used to set about analyzing it. The results obtained will then have a great generality and will not require the adoption of simplified models of the systems considered. The thermodynamic approach is valid for any systems that are sufficiently large for fluctuations of their individual microstates to be smoothed out and not too far from equilibrium to enable the nonlinearity of the processes occurring to be neglected. THEORETICAL BASIS OF THE APPROACHLet us consider a thermodynamically open system that consists of physically and chemically inhomogeneous elements which are ordered in a specific way and are specifically related. The lifetime of the elements exceeds the duration of the functioning cycle of the system. This is a general condition for any technogenic systems which contain sensible components or structures. The behavior of these slowly relaxing elements is determined by the structure of the system. By structure we mean the method of organizing the elements and the nature of the coupling between them. Real systems detect the presence of spatial and temporal structures coupled to a dynamic system. The system as a whole, and also the indeterminacy inherent in it, can be characterized by the number of possible states and by the partial probability of realizing these states that fluctuate randomly with time. The syste...

Nonequilibrium Statistical Operator for Systems of Finite Size

“…It is important to give physical interpretation of the mathematical definition (1). The lifetime of system is related to the time of steady existence of a system, that is to the time of its stay on a homeokinetic plateau whose distribution, for example, in work [2] is compared to entropic and information characteristics of system far from equilibrium, its response to external and internal influences, to stability and adaptive abilities of system. The states of a system on a homeokinetic plateau are characterized by mutual compensation of entropic effect related to the dissipation of energy, and by negentropic effect due to the presence of negative feedback.…”

“…Thus there is one more temporary smoothing in the sense of Кirkwood [41], where a history of system and details of its behaviour at the previous moments of time is specified. I.e., the relation similar (7), defines system with nonequilibrium function of distribution ρ (2) , where lnρ (2) …”

“…For example, in the expression of average values of fluxes through function of distribution ρ (2) there occur additional terms in comparison with similar expressions through function of distribution ρ (1) [20].…”

“…If from ρ (1) (in (30)) we change to ρ (2) (in the formula (28)), the form of (30) will not change, but the values F m (x,t) and X m (x,t-y) will be replaced …”

“…Let's assume that f=2, that is <Γ (1) >=<Γ (2) >. To justify this assumption one can note that the contribution of change of value <Γ> is given by non-stationary processes, non-stationary periods in a history of system, when d S (t)/dt≠0.…”