Some aspect of a system is symmetric if that aspect of the system remains invariant under some transformation. The most fundamental symmetry is CPT symmetry.
Charge (C) - Does the system remain unchanged if we change the sign of the system's charge?
Parity (P) - How does the system change if we change the sign of a single spatial coordinate?
Time (T) - Does the system change if time were reversed?
As far as we know, all systems obey CPT symmetry. To answer your question, we would need to see whether a system has some sort of symmetry associated with it. If a system remains invariant with respect to time, say, then that system has a symmetry associated with time.
Noether's Theorem makes a 1-1 correspondence between conservation laws and symmetries. For example, energy conservation is due to the time invariance of systems. As for "conservation of information law". If this is the law that Dembski proposed, he is full of crap. His reasons for proposing such a law is his opposition to biological evolution.