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The explanation generally used is that every spontaneous process results in an increase in total entropy that is, the entropy of the universe and that thermodynamics therefore does not deny the possibility that a part of the system may become highly ordered if the rest of the system undergoes an increase of entropy that compensates for the local decrease in the ordered sector.
(6) We define the ordered sector as mathbb{S}=[underline{w}, overline {w}]times[underline{z}, overline{z}]=bigl{ (w, z)inmathcal {E}timesmathcal{E}: (underline{w}, underline{z})leq w, z)leq (overline{w}, overline{z} bigr}.
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Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com