What is negative entropy?
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Negative entropy is a term that does not and cannot exist. All the other answers here so far and your question itself are confusing entropy with change in entropy, which are very different. A system with perfect order with only one possible microstate at 0K has zero entropy. There is no system that can have negative entropy, because you cannot have negative absolute temperatures or a negative number of possible microstates.
Also, absolute entropy in general is not a term that is used or has much use at all. What is used is delta(S), the change in entropy during a process. Change in entropy can be positive, negative, or zero. Negative change in entropy indicates a decrease in disorder, or more precisely a decrease in the number of possible microstates available.
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