International Encyclopedia of Systems and Cybernetics

"A time-independent state of an open system in which all macroscopic quantities remain constant, although microscopic processes of the input and output of matter go on continuously" (I. BLAUBERG et al., 1977, p.47).

L.von BERTALANFFY describes the steady state in the following way: "An open system may attain (certain conditions presupposed) a time-independent state where the system remains constant as a whole and in its phases, though there is a continuous flow of the component materials" (1969, p.71)

"Time-independent" seems unfortunate semantics. (see hereafter)

BERTALANFFY adds however: "Steady states are irreversible as a whole, and individual reactions concerned may be irreversible as well. A closed system in equilibrium does not need energy for its preservation, nor can energy be obtained from it (NOTE: This is indeed the isolated system, perfectly disordered in its final state, as prescribed by the 2nd. principle of thermodynamics).

"To perform work, however, the system must be, not in equilibrium, but tending to attain it' (Ibid).

(The German term for steady state, introduced by BERTALANFFY, is Fliessgleichgewicht).

BERTALANFFY, in coincidence with PRIGOGINE, states: "a) Steady states in open systems are not defined by maximum entropy, but by the approach of minimum entropy production. b) Entropy may decrease in such systems. c) The steady state with minimal entropy production are, in general, stable. Therefore if one of the systems variables is altered, the system manifest changes in the opposite direction. Thus the principle of LE CHATELIER holds, not only for closed but also for open systems"(1969, p.78).

No steady state can be maintained without a continual expenditure of energy. Such energy must be obtained from the environment and is degraded as it is used by the system in order to maintain its functions and structures.

As observed by E. LASZLO a steady state system should be clearly distinguished from a static one.

In LASZLO's words: "… steady states are not static states, but ones which represent a level of equilibrium between the internal constraints among the systems components and the forces acting on it from its environment. KATCHALSKY and CURRAN have shown that systems characterized by fixed internal constraints and exposed to unrestrained forces in their environment tend to produce countervailing forces that bring them back to the stable states, since the flow caused by the perturbation has the same sign as the perturbation itself".

This is a kind of generalization of LE CHATELlER Principle to dynamic systems. It implies that steady-state behaviors are periodic, or at least quasi-periodic (no living system could be static and survive).

LASZLO also proposed to replace "steady" state by "optimum" states, but he was not followed (1974, p.50).

BLAUBERG, SADOVSKY and YUDIN state: "Under certain conditions an open system may reach the steady state, as opposed to a closed system which, left to itself, must reach the state of equilibrium" (1977, Ibid).

However some caveats are required:

1/ -Equilibrium is static or dynamic. A static equilibrium would imply a total absence of movement, at least at the observation level. A dynamic equilibrium admits fluctuations around an average level.

2/ -A steady state is possible only in an open system (which admits flows of inputs and outputs). As to the "closed" system referred to, it should be better semantics to call it "isolated" system, (i.e. the purely abstract system in which the 2nd. Principle of thermodynamics strictly reigns).

3/ -"Macroscopic" and "microscopic" should be precisely stated in each case.

4/ -"time-independent" should not be understood as "outside the flow of time", which is obvious within the frame of thermodynamics of irreversible processes.

D. KATZ and R.L. KAHN state: "Though the tendency towards a steady state is in its simplest form homeostatic, as in the preservation of a constant body temperature, the basic principle is the preservation of the character of the system. The equilibrium which complex systems approach is often that of a quasi-stationary equilibrium, to use LEWIN's concept (1947). An adjustement in one direction is countered by a movement in the opposite direction and both movements are approxiomate rather than precise in their compensatory nature. Thus a temporal chart of activity will show a series of ups and downs rather than a smooth curve" (1969, p.97).

→ State (Stationary)