Is Entropy Backwards? Is it weird that everything with a gradient goes from high to low except for entropy? 
High pressures try to fill in low pressures, high temp goes to low temp, osmosis happens from high to low, etc. etc. There are all these examples from things going from high gradient to low gradient to reach equilibrium... except entropy. Are we thinking about entropy wrong or is the key actually because the aforementioned processes are striving for equilibrium, but entropy isn’t in the same way?
 A: Indeed entropy can be confusing (no pun intended). Chapman's examples all involve processes and the disequilibrium that cause them. Entropy is not a process, but a state function just like temperature, pressure, internal energy, enthalpy, etc. 
LightingNe002 statement that "not all processes result in entropy increase" is correct if one looks only at the "system" or only at the "surroundings". However, all real processes are irreversible and result in an overall increase in entropy (system + surroundings). 
I like to use the following heat transfer example to show the connection between entropy and disequilibrium (in this case, thermal disequilibrium). It involves a decrease in entropy of the system, an increase in entropy of the surroundings, but always in increase in the total entropy (system plus surroundings).
Consider a system H (a hot body) and its surroundings C (a cold body). Further consider both H and C to be thermal reservoirs, that is, they are so massive that a heat transfer between them doesn’t change their temperatures. The temperature of H is TH and the temperature of C is TC. We bring the bodies together and desire to transfer heat Q from H to C. Since the temperature of either does not change, the heat transfer occurs isothermally.  Let’s look at the entropy changes:
For Body A (System):  ΔSA = -Q/TH (a drop in entropy)
For Body B (Surroundings):  ΔSB = +Q/TC (a rise in entropy)
The total entropy change:  ΔSTot = ΔSA + ΔSB  
Then for any TH > TC:     Q/T C - Q/TH > 0 
In order for the total entropy change to approach zero, the temperature difference must approach zero.  This results in the heat transfer rate approaching zero and the time it takes to transfer Q infinitely long. In order for the total entropy change to actually equal zero, the temperatures would have to be the same- but if that were the case we would have no heat transfer at all! 
A: Entropy is definitely one of most confusing entities in the realm of Thermodynamics(at least I fount it to be so).Coming to the heart of the matter, not all processes result in an increase in entropy. For example when a stretched rubber band comes back to original form entropy decreases. And there are infinitely more processes where Entropy decreases. 
The thing is this is how we defined Entropy. We could have  named it something else and decided that when entropy decreases this quantity decreases.Entropy increases even though pressure tends to decrease as we approach equilibrium because we made it like that.
Also the sole purpose of these quantities is to help us determine spontaneity,feasibility,energy change,etc associated with a given process.Reaching Equilibrium for a system means maximization of Entropy,bringing Gibbs Free Energy to zero,having no Temp difference w.r.t surroundings and having Chemical Equilibrium.
And if you think equilibrium means minimization of all variables then delete this thought. Think about unstable equilibrium to justify my previous statement.
