The Thermodynamics of Symmetrical Bodies

Boltzmann

Flasks with Cohorts

Albert Einstein's "Electrodynamics of Moving Bodies" did encompass symmetry into some mind blowing theories on space and time and what not. But let us remind ourselves, we are humble people in the pursuit of answers in chemistry. But I do conjure up Einstein's miracle year papers to prove my point of the importance of symmetry.  Boltzmann (the handsome devil whose picture is shown above) had a way to calculate entropy based on the number of macro states a substance (let's say gas) can occupy in a cohort. The flasks with their cohorts are also above. There is a way to calculate entropy; it is S=klnW. S is entropy, k is Mr. Boltzmann's constant, and W is the number of macro states. There is a ubiquitous correlation between symmetry and entropy. Entropy very much is a degree of symmetry. Because there are two types of symmetries( dynamic entropy and static entropy) there are two types of entropies, aptly named dynamic entropy and static entropy. 

Everybody, just relax. I'm going to explain the two. Dynamic symmetry is due to dynamic motion like the motion of one individual molecule and static symmetry is due to phase change. It is obvious, looking at the cohorts, that III has more macro states and greater symmetry (the one that has the statistically better chance at happening). A symmetry increase due to dynamic motion is just as apparent. An electron flying in its orbital leads one to conclude that the hydrogen atom is a symmetrical sphere. If the electron did not move as it did, the atom would not be seen as a sphere because of the definite spot of the electron.  

Change in Gibbs free energy can measure whether some process is spontaneous or not. If it is negative, it is spontaneous, if it positive then it is not, and if it is zero then it is at equilibrium. This is the max entropy. At this state, the substance is most susceptible to some internal or external constraints. Constraints like this include polarity and isotropicity. When these changes happen, because of a force or field, the symmetry is reduced as well as the entropy. Our friends in Basel, Switzerland have come up with the perfect platitude: Any system evolves spontaneously toward a maximal symmetry. It is analogous to saying that when I heat up a gas, the entropy is increased because of the higher number of possible arrangements these molecules can be in. But, contrary to common sense and intuition and thermodynamically speaking, the symmetry increases because individually each molecule has more energy and that little electron is moving a lot faster allowing the nuclei of the molecules to look more like spheres. But there are real irking (I like the work irk) constrains like I just mentioned. The van't Hoff factor (bringing these gas molecules closer together and restricting their degrees of freedom) are the constrains that reduce the symmetry. The point is that that these gas molecules are indistinguishable from one another and that is why the apparent disorder has nothing to do with our discussion on symmetry. I can attest to the fault reasoning that symmetry is disorder. We can say a sphere is perfectly symmetrical because if we rotate it an infinite number of ways, it is distinguishable from all views.  Mathematically, it boils down to this equation: S=lnN! where N! is the total permutation symmetry number.  We have all heard about the heat death of the universe, where the universe (as entropy inexorably increases) will stop at the point where entropy of the universe is maximum. This goes along with the Big Crunch Theory of the death of the universe where the reverse of the Big Bang will happen, essentially. In the fist scenario, the entropy of the universe is max. and in the second, the symmetry of the universe is max. (as everything will be in the singularity). Both are end of universe scenarios (how poetic).  Hope you have enjoyed this look into the relationship between entropy and symmetry (for a while, people have been asking me what's their story, you know are they dating or something but it hasn't been until now that their relationship has been explained in terms of end of time scenarios).