Statistical mechanics

[TinyTree]

I am trying to put together a new article on "the probability of the universe" but it takes time.. so I am thinking of just posting some thoughts here, and I may lift out of these and put them into an article once I get some cycles together.

One main issue is discerning the difference between statistical mechanics and the the probability of the state vector. When one thinks of the probability of a physical system, one immediately thinks about the entropy of the universe. So how can we clarify this in your mind?

Statistical mechanics describes the probability of a system being within a partition. The system phase space is partitioned- broken into a set of disjoint yet mutually exhaustive states. Then the question becomes: what is the probability of the system residing in one of these partitions? It is a combinatoric question.

The laws of thermodynamics follow from the laws of large numbers in statistics and the combinatorics within. Thus, implicit in the understanding of statistical mechanics is the matching of multiple microstates to be equivalent. This is true for measuring a thermodyanmic property. However, it is not true unto the state itself- that is, a set of molecules with a specific exact configuration is actually not the same as a different specific configuration. They have the same temperature, mass, heat, etc, but they are not the same configuration. It must be understood that these are distinct configurations- not from a macroscopic observable, but on an intrinsic level are separate microstates, for one to apprehend the probability of the state vector of a system.

The critical underpinning thought of statistical mechanics is the ensemble- a collection of microstates having an extensive property in common. It is this extensive property which holds the probability for the system.




http://72.14.203.104/search?q=cacheWFjUGQuPt8J:www.cheme.buffalo.edu/courses/ce530/Text/StatMech6c.doc+partition+phase+space+statistical+m echanics&hl=en

[mkirkpatrick]

It all sounds very complex to me,micro-states,are these mini-worlds much like
an atom within its tiny solar system,and if so then they would be all linked,is that right.I keep remembering the phrase "there are lies,dam lies.and then there
are Statistics".Can it be made simple I ask.




kind regards michael.

[TinyTree]

It all sounds very complex to me,micro-states,are these mini-worlds much like an atom within its tiny solar system,and if so then they would be all linked,is that right.

The language I used in that note is the language of statistical mechanics- I am not particularly fond of those words myself, but if someone reading it is trying to understand the relationship of the probability of a state vector to the entropy of a system it should help them understand the difference.

The important point to understand is that entropy DOES NOT REFER to the absolute probability of the system- it does refer to the probability of the system being in one of many "identical" configurations- where "identical" is in quotes because it refers to a macroscopic measurement, like temperature.

So microstate means "complete description of every aspect of every constituent of the system". The macrostate consists of many microstates. That is to say, lets us look at some words- and we will use the "macroscopic quality" of number of e's:

betterment (3)
feelings (2)
hehehe (3)
ourhouse (1)
extrapolate (2)
formula (0)

So you can see that the words "betterment" and "hehehe" have the SAME VALUE. If you were measuring these words, and could only measure the e's in words words- then you would consider these two words "betterment" and "hehehe" TO BE THE SAME THING. They are the SAME THING MACROSCOPICALLY WITH A MEASURE OF E's, but obviously are not the same word.

The underlying thesis of this whole theory is that the two words are not the same thing! They are different words! The microstates (the individual words) correspond to just a few macrostates (either 0,1,2 or 3 letter e's)

So I am trying to tell you that entropy is a measure of the number of e's essentially, and I am pointing out that the words are actually different words- and further by understanding they are different words we can understand the nature of the entire evolution of the universe on a more fundamental level.

Does this alternative approach make any sense? It is more of an analogy than an absolute mathematical relationship, but it is a very close analogy.


The fundamental nature of the system is as follows:

There are nondeterministic probabilistic events

These events can "get stored" in the universe by landing in a self preserving configuration

They can propagate into the future

The most striking examples of this are:

- The gravitational precipitation points of the original stars, which broke the symmetry of the early universe (presumably virtual particles as understood in the theory of Quantum Electro Dynamics)

- Living organisms, in their DNA as it propagates itself into the future

- Culture itself- which is a self propagating phenomena through interorganism communication. Our culture is an example of propagating nondeterministic events. Accidents which are observed and remembered create ideas that are transmitted from one organism to another. The experiments which go on in thinking through potential futures within the mind are another example.

- Mathematics itself, as a logical system, can be shown to have its origins in probabalistic phenomena (if we go to the formal systems of Whitehead and then look at irreducible truths outside of the axiomatic framework of a mathematical system). This will take some more research to show compellingly, but I hope to address it at some point.

I keep remembering the phrase "there are lies,dam lies.and then there
are Statistics".

Yes, I think the reason that this theory has not been mainstream (in the regular scientific though) is that the mathematics behind statistical mechanics are difficult enough to approach that most people just say "oh, okey dokey" and then turn off the further questioning of "Is statistical mechanics a complete representation of the probability of a system?" and the answer is "No, although it is complete unto itself, but it fails to represent all of the aspects of the probability of mathematical and physical systems."

Can it be made simple I ask.

Thanks for making the effort to understand it. Please ask lots more questions and perhaps I can address them effectively enough that I can communicate this idea in a comprehensible way.