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The local form of the second law of thermodynamics
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The precise formulation of the second law is that the local mean 
entropy production is always nonnegative. 


Local entropy production is a technical term and describes only that 
part of the local entropy change that cannot be explained by entropy 
flow. It is this term that the second law requires to be nonnegative 
(in a classical setting interpretable as the amount of information 
irreversibly lost to the neglected microscopic degrees of freedom), 
no matter how much entropy flows in or out the system.
 
Thus thereere are two processes affecting the entropy distribution: 
1. local entropy production, and 
2. flow of entropy. 
The former is nonnegative at all places (this is the second law), 
whereas the latter redistributes the entropy between places in a 
conserved fashion. Entropy flow is unconstrained by the second law; 
therefore the entropy can decrease easily in open nonequilibrium 
systems (which exchange matter, enrgy, and entropy with the 
surrounding).
 
For example, in fluid flow, local entropy production is associated 
with dissipative terms in the Navier-Stokes equations. Neglecting the 
entropy production results in the Euler equations. The latter are 
conservative but have an entropy current, which - unlike with 
Navier-Stokes - together with the entropy density satisfies the 
continuity equation.
 
All this can be read in books on nonequilibrium thermodynamics. 
My favorite book is Reichl's Modern Course in Statistical Mechanics.


In Nature, there are many processing creating low entropy locally.
When ice freezes, lots of entropy is transported to the surrounding 
to create the crystalline order; but the local entropy production is 
still positive. The low entropy of biochemical substances is also a 
result of an entropy current during their formation that dominates the 
(still positive) entropy production.