Second law of thermodynamics and absolute zero

[i_hate_math]

Does a system with zero entropy represent the thermal equilibrium at some temperature = 0K? Does the second law of thermodynamics entail that the system will eventually evolve to higher entropy?

e.g. a system of 7 magnetic dipoles of paramagnetic spin-1/2 particles in an external magnetic field . Does the microstate of 7 spin-up (or 7 spin-down) represent thermal equilibrium at temperature T = 0K, since its multiplicity = 1, hence entropy = 0? Or will the mighty 2nd Law tell the system to create more entropy?

 

[jfizzix]

The second law is a statistical law.
If the system of dipoles is completely isolated so that it cannot exchange energy with the environment, then the zero entropy state may remain so indefinitely. The same is true for all other constant values of entropy.

However, if the system can exchange energy with the environment, then there are random exchanges of energy between system and environment, and because higher-entropy states are much more likely to exist at random than low entropy states, you will see the entropy increase until the temperature of the system and environment are equal.