Second Law of Thermodynamics

The inequality S_{universe} \ge 0 means that every real process in an isolated whole system produces entropy or, at best, leaves it unchanged in an ideal reversible limit. This comes from the statistical fact that there are vastly more disordered microstates than ordered ones, so spontaneous change overwhelmingly tends toward higher total multiplicity. In thermodynamics, the "universe" means the system plus everything interacting with it, so even if one part becomes more ordered, the surroundings must gain enough entropy to make the total nondecreasing.

Use this law when deciding whether a process can happen spontaneously and when checking the direction of heat transfer, mixing, friction, phase changes, or chemical reactions. It is also the key rule for identifying reversible versus irreversible processes in advanced thermodynamics.

• Using the formula for a single object only, instead of the total entropy change of system plus surroundings
• Forgetting that entropy can decrease locally as long as the surroundings increase by a larger amount
• Treating \u0394S_universe = 0 as the normal case for real processes, when it only applies to ideal reversible processes