Joined: June 2006
By the common view of the SLOT, I assume you mean the general:
"Things don't go from disorder to order"
The second law in general is:
"A closed system with a specific internal energy will tend to relax (each subsystem will approach the average internal energy) and will occupy the most probable state."
Entropy itself is a function of the internal energy of the system, the volume the system occupies, and the number of particles in the system. It's a dimensionless number, it has no units (like meters, or degrees Celsius).
Let's say system A has 6 possible states, system B has 10, possible states, then there are 60 (6x10) possible states for the two together, AB, easy enough.
The entropy of a system is the natural logarithm of the number of states. It turns the total states from a multiplicative quantity (6x10) into an additive quanitity ( ln(6x10) = ln(6)+ln(10) ). The total number of states can be calculated from classical and quantum mechanics. I won't go into the details here (relates to something called phase volume), since it doesn't have much bearing on the point I'm trying to make.
The second law says that the number of states in A will increase and the number of states in B will decrease until they come to an equal quanitity (6->8 10->8). The total number of states then becomes (8x8) = 64, thus the total entropy will then go from ln( 60 ) to ln ( 64 ). Notice that the entropy of B actually decreases in the process, from ln(10) ->ln(8), which you might think violates the second law, but since B is not in thermal equilibrium with A, this is perfectly legal.
edit - added phase volume info
edit - removed old tag