Wednesday, June 29, 2022

CMA Sequences & Structures vs. Microstates & Macrostates (Extreme Math Card Magic)

Recall that during our last class video we worked through several applications of the klein8 group v8 but before we go more deeply into the group v8 and on from there to the klein 16 group b16 i would like to explain that because much of what i have presented in these class videos.

Is original work choices had to be made regarding vocabulary terminology and notation for new ideas consequently i feel mathematically compelled to share the following observations some of which involve vocabulary and terms.

From the study of statistical mechanics so what we're going to do is we're going to explore how i have been using the vocabulary that i've created and how it can be translated into the vocabulary of statistical mechanics more specifically into the notions of.

Macro state and microstate okay so as stated here cma sequences as used above should perhaps be called something like cma sequence.

Configurations why is that because each cma sequence as i have been using the term is really a sequence configuration or a sequence form where each of these sequence configurations or sequence forms have more than one.

Particular expression or incidence or a manifestation or specific outcome for example we have been saying that there are two cma sequences of order four having cma structure type s-o-o namely the following.

But since we are assuming the two zeros are in fact distinguishable and that the two ones are distinguishable the actual number of cma sequences and that's in quotes for a specific cma structure.

Of order four is eight not two this is because there are two cma configurations of order four namely one zero zero one and zero one one zero each yielding four distinct.

Cma sequences to see this simply add subscripts to the two zeros and to the two ones and you will get this list of specific cma sequences in general if there are m zeros and m ones in a particular cma.

Configuration then the total number of cma sequences having that configuration is m factorial squared times the number of cma configurations moreover none of these specific cma sequences above namely these eight right here is actually fixed.

By any non-identity group element the only things that are fixed or inverted are the cma configurations such as one zero zero one or zero one one zero or the cma structure types themselves namely s-o-o as a structure type in the.

Language of statistical mechanics we can say the universal set is as follows 0 sub 1 0 sub 2 1 sub 1 and 1 sub 2. of course the total number of permutations of these four distinct objects is 4 factorial which is equal to 24. now if you think about the cma structure.

Types they are actually macro states in the language of statistical mechanics there's three of them s o o o s o and o o s and for each of these three.

Macro states we have eight microstates for example the following are the microstates for the macrostate soo these are the same eight cma sequences listed on the previous page notwithstanding all of the above.

Qualifying observations i will continue to use the more parsimonious terminology that i have used from the beginning of my introduction of cma structures and cma sequences the principal issue for the reader to understand is that when i use the term.

Cma sequence in general i am actually referring to an entire class of individual sequences having a specific cma structure.

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