Entropy / Structure Relations I want to check on the validity of the following objective definition of order. Is it correct? Is there a more rigorous statement of this concept? 
The further a system is from its maximum thermodynamic entropy, the more ordered it is and the lower its entropy. Specifically, if a system’s microstates are not of equal probability, which is usually the case because of interactions or correlations between the microstates, it is more ordered when it spends time in the less likely states. If the microstates are of equal probability, it can be constrained to remain in one of the states a disproportionate amount of time by imposing constraints on the system’s random fluctuations. 
Thanks very much for the input.
 A: This definition is not correct. A thermodynamic state $A$ of a particular system is said to be more ordered than another thermodynamic state $B$ of the same system if $A$ is invariant under less symmetry operations than $B$.
The entropy of a thermodynamic state of a particular system, on another hand, quantifies the number of microstates which are compatible with the said thermodynamic state.
It is clear from these two definitions that the definition of entropy does not entail that higher entropy equates higher disorder.
It so happens that in most cases in fact, higher number of symmetries allows for higher number of states and hence higher entropy but it is not always so.
Hard sphere systems (which do not have any energy scale) have been shown to have a fluid/solid transition above a certain packing fraction for instance. In this case, at high packing fraction, it is less constraining for the spheres to adopt an ordered structure than trying to satisfy invariance under any rotation and any translation; the obtained crystalline structures have then higher entropy than the disordered ones. The same goes for hard rods which, above a certain packing fraction display an entropy-driven phase transition from isotropic to nematic.
Morality, it is not wise to identify entropy with disorder as they do not assess the same features of a given thermodynamic state of a system.
A: Before answering, I would ask where that definition is from.  Is it a reference to a statement you found in a text? if so which one?  And what are your criteria for 'rigorous' i.e are you asking for a METHOD by which to check, or are you asking for a consensus on if it rigorous/ not?  
Of the bat though, without a context, the second part is suspect to me.  I'd consider it to be self evident that if constraints are placed on 'random' fluctuations, the micro-states really are no longer of equal probability.   ...BUT,  perhaps they are viewing the constraints in regard to a system that usually has states of equal probabilitu interacting with an 'outside' influence.  So, as I said, it would be useful to have a context.  I suppose my criteria for 'rigourous'  demands greater context, so my answer right now is 'to be determined.'
