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Since free neutrons want to undergo beta decay into a proton while protons are relatively stable does that mean that neutrons have higher entropy than protons?

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    $\begingroup$ Having a higher entropy would lower the Gibbs free energy of the neutron (of course, ignoring the enthalpy difference). I'm confused on the reasoning in your question. $\endgroup$
    – Jon Custer
    Commented May 30 at 13:54
  • $\begingroup$ In a closed system, entropy always increases. This means that if neutrons had a higher entropy than protons, they would not decay into them. $\endgroup$
    – paulina
    Commented May 30 at 14:25
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    $\begingroup$ (not to mention that entropy is a statistical phenomenon which is used to describe many-body systems. applying it to a single neutron may be possible in relativistic QCD, but i am not sure if it would yield useful results) $\endgroup$
    – paulina
    Commented May 30 at 14:29
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    $\begingroup$ @paulina - Note that there is entropy in the electron and neutrino states too. If that is big enough then a high entropy neutron could decay into a lower entropy proton. However, I don't think this is a likely case. $\endgroup$
    – Anders Sandberg
    Commented May 31 at 11:01
  • $\begingroup$ It almost seems that this depends on the strength of the gravitational potential. In a neutron star, the neutron is stable, whereas electrons and protons cannot exist or are at least the unstable objects. Interesting question, thanks for that. $\endgroup$
    – HolgerFiedler
    Commented Jun 2 at 4:47

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