A simple definition of entrophy and how it relates to chaos theory?

Answer 1

Entropy is the amount of Energy that is not available for work during a certain process and in other words the energy form of a system that relates to its internal state of disorder, (high entropy levels are disordered states, low entropy levels are characteristic of ordered states).Entropy in general is based on the SECOND LAW OF THERMODYNAMICS.As far as entropy and the chaos theory is concerned there is a very simple connection.Nothing happens without making the universe a bit more disorganised, in general there is a tendency of available energy to dwindle (it is true that in some billion of billion of years there will not be any more energy in a form that we can use) and entropy is a measure of the systems-universe disorder.Have a nice day.

Answer 2

Define Chaos Theory

Answer 3

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A simple definition of entrophy and how it relates to chaos theory?

Answer 4

Entrophy

Answer 5

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Since all the initial conditions cannot be known, in complex systems complete predictability is impossible to attain. The result is apparent "chaos" (unpredictability) even though the system in question is fully complying with the known rules of physics. The obvious example is weather, which man has struggled to predict throughout history, but since we cannot know every fluctuation in surface temperature, every eddy in the wind cycle, and every localized disturbance (a large bonfire, for example) we can only predict weather to a limited degree for a relatively large land area (not at all for, say, your yard).

Answer 6

entropy is a measure of randomness/order/disorder. one of the things that chaos theory addresses is finding order in what was once thought to be complete disorder (chaos)

Answer 7

The simplest definition, I suppose, is the tendency of all matter and energy to decline into a state inert uniformity. [1]

In everyday parlance we use the term to refer to inevitable disintegration of order into disorder.

Originally derived from thermodynamics, it has come to have parallel meanings in physics, chemistry, statistics, information theory, communication systems. In cosmology, it refers to "a hypothetical tendency for the universe to attain a state of maximum homogeneity in which all matter is at a uniform temperature"; in other words heat death, or absolute chaos resulting from no energy being available for use. By analogy, in information theory, it has come to be associated with "a measure of the loss of information in a transmitted signal or message," or the relationship of noise to information. [2]

Over forty years ago I read a fascinating book by one of the pioneers in cybernetics and computer science. It is called The Human Use of Human Beings by Norbert Wiener, and it has one of the most elegant, simplest, and (in the long run) most hopeful statements about entropy and chaos theory that I have ever read:

"As entropy increases, the universe, and all closed systems in the universe, tend naturally to deteriorate and lose their distinctiveness, to move from the least to the most probable state, from a state of organization and differentiation in which distinctions and forms exist, to a state of chaos and sameness. In [this] universe order is least probable, chaos most probable. But while the universe as a whole, tends to run down, there are local enclaves of whose direction seems opposed to that of the universe at large and in which there is a limited and temporary tendency for organization to increase. Life finds its home in these enclaves. It is with this point of view at its core that the new science of Cybernetics began its development."

I have kept this statement in my mind throughout my career (and life). I recommend that you read Wiener's book. First published in 1950 [2nd ed., 1954], it is still fascinating reading today.

The subtitle of the book is Cybernetics and Society. Wiener's focus is on the social implications of entropy/chaos and especially those "local enclaves" in which order, not disorder, is gaining ascendancy.

"A clear understanding of the notion of information as applied to scientific work will show that the simple coexistence of two items of information is of relatively small value, unless these two items can be effectively combined in some mind or organ which is able to fertilize one by the means of the other.

"This is the very opposite of the organization in which each member travels a preassigned path..."

All learning, all teaching, our very survival, depends upon the juxtapostion and combination of two items of information so that they "are able to fertilize" one another. Our survival as humans depends upon our celebrating and maximizing this "temporary tendency for organization to increase." Wiener welcomed us to the Age of Information.

. . . . . . . . . .

"The lives of great men all remind us
We can make our lives sublime,
And in departing leave behind us
Footprints on the sands of time."