Saturday, May 6, 2017

statistical mechanics - Second law of Thermodynamics: Why is it only "almost" always true that entropy is non-decreasing?



Wikipedia - Second law of thermodynamics:



...the entropy of any closed system not in thermal equilibrium almost always increases.




I understand that the second law of thermodynamics is based on the statistical unlikelihood of fast-moving molecules to aggregate.


However, if it is only "almost always" then why is the phenomenon stated as a law?


Is it because we have not yet observed the unlikely aggregation?



Answer



I think the author has used the word "almost" to incorporate the possibility that $ \Delta S $ can be equal to zero also. As the exact statement of second law of thermodynamics goes this way,


An isolated system evolves in such a way that $ \Delta S \geq 0 $.


This means that an isolated system should evolve in such a way that the multiplicity should remain same or increase.


For example, consider a simple system with two macrostates $A$ and $B$, with $4$ and $6$ microstates respectively. If we find the system in mactrostate $A$, it can evolve and remain in same state or can move to macrostate $B$. But, if we find the system initially in macrostate $B$, it will remain in macrostate $B$ and never trasits to macrostate $A$.


To my knowledge, no one knows why nature follows this rule!!!


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