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Spontaneous symmetry breaking (SSB) occurs when the state of a system possesses less symmetry than the underlying laws governing it. This raises the question: What happens to the entropy of the system during the SSB, from both quantum and classical perspectives? Does the second law of thermodynamics hold during SSB, or is it irrelevant? Additionally, spontaneous symmetry restoration (SSR) is often discussed in the literature and may occur after SSB. In classical physics, SSR is typically forbidden due to the second law of thermodynamics. Another question arises: Why does SSR occur, and how is the system's entropy affected by it and also, in general, during the SSB followed by the SSR?

Looking forward to hearing your insights on these matters. Thanks.

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  • $\begingroup$ Spontaneous symmetry breaking (SSB) occurs when the temperature falls below a critical threshold. Consequently, in a very approximate sense, the number of accessible states decreases, leading to a reduction in entropy. $\endgroup$
    – Bababeluma
    Commented Mar 8 at 16:47

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In the context of phase transitions, broken symmetry means that the system has no time to explore all the possible configurations: e.g., probability of ferromagnet reversing its magnetization is too small to be realistically taken into account on reasonable timescales (like the duration of the experiment, human lifetime, existence of humanity, lifetime of the Universe.) Thus, the system is not in thermodynamic equilibrium, and it doesn't make sense to speak of the second law.

Note also that from this (classical thermodyanmics) perspective symmetry breaking is not a process, but simply characterization of an existing state, so it doesn't make much sense to talk about how entropy changes when the symmetry is broken.

If the probability of transitioning to alternative configurations was not negligibly small, such a transition would eventually occur, i.e., the system would reach equilibrium, and its entropy would increase (as it now occupies larger phase space.)

Related: Why don't we observe spontaneous symmetry restoration in nature?

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There is no direct and unique relation between the symmetry of thermodynamic phases and entropy. The presence of reentrant phase transitions (as a function of temperature) from more "less ordered" to "more ordered" and back to "less ordered" phases, like in adsorbed monolayers, liquid mixtures, and liquid crystals, is evidence for the previous statement.

Notice that there is no reason to distinguish between quantum or classical perspectives.

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