Saturday, 31 August 2019

thermodynamics - Is a world with constant/decreasing entropy theoretically impossible?


We can imagine many changes to the laws of physics - you could scrap all of electromagnetism, gravity could be an inverse cubed law, even the first law of thermodynamics could hypothetically be broken - we've all imagined perpetual motion machines at one time or another.


However, the second law of thermodynamics seems somehow more 'emergent'. It just springs out of the nature of our universe - the effectively random movement of physical objects over time. Provided you have a Universe whose state is changing over time according to some set of laws, it seems like the second law must be upheld, things must gradually settle down into the state of greatest disorder.


What I'm particularly wondering is if you can prove in any sense (perhaps using methods from statistical mechanics)? Or is it possible to construct a set of laws (preferably similar to our own) which would give us a universe which could break the second law.



Answer



The short answer is that such a universe cannot be envisaged, not with relevance to our known physics.



Entropy as defined in statistical thermodynamics is proportional to the logarithm of the number of microstates of the closed system, the universe in your question. You would have to devise a universe where the number of microstates diminishes with time.


The great multiplier of microstates in our universe is the photon, which is emitted at every chance it gets, and thus increases the number of microstates. Photons are emitted by electromagnetic interactions and by all bodies consisting of atoms and molecules due to the black body radiation effect. Each emitted (or absorbed, because the state of the atom that absorbed it has changed) photon defines a new microstate to be added to the number of microstates, whose logarithm defines entropy. A universe without electromagnetism would not have atoms.


It is worth noting that all biological systems decrease entropy, as does the crystallization of materials, but this is possible because the systems are open and the energy exchanges create a large number of microstates thus obeying in the closed system the entropy constraint.


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