Is entropy maximized or increasing? Do different real processes involve different rates of change of entropy? (Is the rate of change of entropy constant with time throughout all regions of space, or perhaps in other words, constant with spacetime?)
What equation describes the relationship between entropy and time?
I know 


*

*$S = k \ln N$, and

*$S = Q/T$


And for intuition, "Entropy quantifies the amount of uncertainty involved in the value of a random variable or the outcome of a random process"
Also, Shannon entropy explains the futility of Maxwell's Demon : 
S = log2 (outcomes)
(ex. S = 2 bits = 2^2 = 4 for the tossing of two coins)
I apologize for being all over the place. I'm just trying to get my bearings here, so any help is appreciated.
Related (vaguely:) Is the Bremermann limit an attractor, repellor, or neither?
 A: Entropy is monotonically increasing with time, but its rate of change can be anything from zero to an arbitrarily large value. 
Lets say you have two boxes, one filled with oxygen and another filled with hydrogen. There is a door between the two boxes but it is closed. In this state, the entropy has a relatively low value and the gases and entropy can stay in this state forever. 
If you open the door between the boxes, then the gases mix. Being mixed up is more disordered than having two boxes with the gases separated. So as the gases mix, entropy increases.  When does the mixing (entropy increase) stop? When the gases are fully mixed together. That is, entropy will continue to increase until it cannot increase any further. So in this sense, entropy tends to the maximum value allowed by your system. You can always bring in another box, containing nitrogen, and let the gases mix again which again increases entropy. This means that no matter how much entropy you have, you can always have more. So in a sense, entropy is never globally maximized (in a finite amount of time). 
Sort of like, no matter how bad it is, it can always get worse!
A: Entropy increases in a closed system.
But, a system can be subdivided into two sections, and entropy can be made to decrease in one section while it increases in the other. 
This is the basis of biological life, and also, refrigerators.
In order to organize one section of a system, another section must become disorganized. Or, in other words, to create order in one space requires the creation of disorder to an equal or greater degree in another space.
So, the answer to the question "Is the rate of change of entropy constant with time throughout all regions of space, or perhaps in other words, constant with spacetime?" is NO.
