## DEGREES OF FREEDOM
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The measure of the leeway of variability in a system.

According to P. BERGE, Y. POMEAU and Ch. VIDAL, a degree of freedom may be understood in two different ways:

- either: "each couple of position-velocity coordinates associated with a possibility of displacement"

- or: "one only of these two elements: position or velocity

"Thus a set of N bodies able to move in the three directions of space presents 3N or 6N degrees of freedom, according to the definition used" (1984, p.13).

The degrees of freedom define the dimensions of the phase space.

H. HAKEN and A. WUNDERLIN equate degrees of freedom with "order parameters". They state:"lndeed, three order parameters or degrees of freedom are enough to make the system chaotic" (1990, p.1250).

It is however to be noted that the degree of correlation in-between degrees of freedom is a very important factor: less correlated degrees of freedom induce chaos much more easily. (see; "frozen core") Or, in other terms, incommensurability is a determinant factor of chaos. The subject seems somehow related to prime numbers.

From another viewpoint, R. ROSEN states: "A functional activity manifested by any particular system typically involves only a few of the structural degrees of freedom of the system" (1974, p.63).

These "free" degrees of freedom are eventually available for other innovative interactions or functional activities of the system (see "Function change").

Degrees of freedom can also be understood in terms of autonomy (in P. VENDRYES' sense): Each internal regulator with counter-aleatory reserves at its disposal, enhances some degree of freedom of the system.

### Categories

- 1) General information
- 2) Methodology or model
- 3) Epistemology, ontology and semantics
- 4) Human sciences
- 5) Discipline oriented

### Publisher

Bertalanffy Center for the Study of Systems Science(2020).

To cite this page, please use the following information:

* Bertalanffy Center for the Study of Systems Science (2020).* Title of the entry. In Charles François (Ed.), International Encyclopedia of Systems and Cybernetics (2). Retrieved from www.systemspedia.org/[full/url]

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