Entropy Operator for Houdini Particles

This site follows my attempts to make Houdini particle operators that deal with Entropy as it related to the measure of the amount of disorder in a system.


 

BACKGROUND

 

What is entropy?

 

Entropy as a measure of disorder

From Wikipedia, the free encyclopedia.

 

We can view Ω as a measure of the disorder in a system. This is reasonable because what we think of as "ordered" systems tend to have very few configurational possibilities, and "disordered" systems have very many. Consider, for example, a set of 10 coins, each of which is either heads up or tails up. The most "ordered" macroscopic states are 10 heads or 10 tails; in either case, there is exactly one configuration that can produce the result. In contrast, the most "disordered" state consists of 5 heads and 5 tails, and there are 252 (10 choose 5) ways to produce this result.

Under the statistical definition of entropy, the second law of thermodynamics states that the disorder in an isolated system tends to increase. This can be understood using our coin example. Suppose that we start off with 10 heads, and re-flip one coin at random every minute. If we examine the system after a long time has passed, it is possible that we will still see 10 heads, or even 10 tails, but that is not very likely; it is far more probable that we will see approximately as many heads as tails.

Since its discovery, the idea that disorder tends to increase has been the focus of a great deal of thought, some of it confused. A chief point of confusion is the fact that the result ΔS ≥ 0 applies only to isolated systems; notably, the Earth is not an isolated system because it is constantly receiving energy in the form of sunlight. Nevertheless, it has been pointed out that the universe may be considered an isolated system, so that its total disorder should be constantly increasing. It has been speculated that the universe is fated to a heat death in which all the energy ends up as a homogeneous distribution of thermal energy, so that no more work can be extracted from any source. Recent work, however, has cast extensive doubt on the heat death hypothesis and the applicability of any simple thermodynamical model to the universe in general. Although entropy does increase in an expanding universe, the maximum possible entropy rises much more rapidly and leads to an "entropy gap," thus pushing the system further away from equilibrium with each time increment. Furthermore, complicating factors such as the impact of gravity, energy density of the vacuum (and thus a hypothesized "antigravity"), and macroscopic quantum effects under unusual conditions cannot be reconciled with current thermodynamical models, making any predictions of large-scale thermodynamics extremely difficult.

 

Possible use for entropy in a procedural particle system

Entropy is also a measure of the amount of energy in a system that cannot be used to do work. This energy escapes from the system in the form of what we could call heat. Generating a Per-Particle temperature attribute that is derived from the amount of disorder in a particle system [the entropy of the particle system] should make it possible to use an Interact POP to push particles away from each other in areas of high temperature. It is possible that a simulation like this might model the behavior of air molecules inside of a flame.

 

Hypothesis

If a value can be generated for entropy, Then using it in conjunction with an interact POP will model the behavior of air molecules in a flame.

 

Generating a value for entropy using a particle system

Entropy is a measure of the amount of disorder. Standard Deviation is a measure used in statistics and probability that appears similar to this.

 

Standard deviation

From Wikipedia, the free encyclopedia.

 

In probability and statistics, the standard deviation is the most commonly used measure of statistical dispersion. Simply put, it measures how spread out the values in a data set are.

The standard deviation is defined as the square root of the variance. This means it is the root mean square (RMS) deviation from the average. It is defined this way in order to give us a measure of dispersion that is (1) a non-negative number, and (2) has the same units as the data.

 

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