I was wondering this. What if particles tunnel to a lower entropy state? Then can that actually decrease entropy, if every particle in the universe so happens to tunnel in a certain way? Or is this simply not possible at all?
1 Answer
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Look at this Quantum Mechanical model of alpha particle tunneling
Note that the particle comes out at the same energy it had in the potential.
So by the definition of $dS=dQ/dT$, one alpha decay will increase the entropy because it will add energy E to the system.
Going to the microstate counting definition of entropy $S=kln(Ω)$ where Ω is the multplicity, alpha particles tunneling increase entropy.
Tunneling takes a particle out of a potential barrier, it does not take it into lower or higher entropy states in particular, but tunneling will always increase the entropy of the system.
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$\begingroup$ An unbound alpha particle can also tunnel into the nucleus, reducing entropy. It is just that it is way less likely since the set of microstates sending it close to the nucleus is tiny compared to the total set, while the bound case is essentially a single micro and macro state. $\endgroup$ Commented Feb 10, 2020 at 9:16