Talk:Spontaneous symmetry breaking in classical systems

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    Reviewer A

    The article is clear and well written. Surely it can be accepted as it is. Personally, I would have reversed the presentation: start from spontaneous symmetry breaking in classical statistical mechanics, which is a well known phenomenon, and then discuss spontaneous symmetry breaking in classical mechanics, as the limiting case at zero temperature. But this is a matter of taste. The different strategy chosen by the Author is surely correct, and the final product is very good.

    Author's answer to reviewer A

    The presentation reflects logical motivations. Starting from spontaneous symmetry breaking (SSB) in classical statistical mechanics would have had the drawback of linking the explanation of the mechanism to the properties of complex systems (a very delicate and deep subject) and in particular would have relied on (the limiting extrapolation of) the thermodynamical limit, since, strictly speaking for a mathematical physics point of view, there is no SSB in classical statistical mechanics as long as the volume is finite.

    The choice was made in order to avoid the risk of obscuring the crucial role of the infinite extension of the system for the occurrence of SSB, a main point of the article. In the author opinion, SSB may be explained also to mathematicians and in general to an audience not familiar with the philosophical subtleties of the foundations of classical statistical mechanics, only a basic knowledge of classical mechanics of finite and infinitely extended systems being required.

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