that's not true at all. Any time you destroy information (for example an and gate can destroy information) you use energy.
If you're willing to explain, I wonder how an AND gate destroys information. Certainly the output of a 2-input AND gate carries less information than both inputs together. But unless the gate is destroying the input signals, which it isn't, I don't see how infomation is being destroyed.
Related topic: reversible computing. You might wonder if a computation need take any energy at all: it turns out that an irreversible computation (e.g. NOR, XOR, AND etc) is physically guaranteed to waste energy, but if you make sure your compute steps are always reversible (i.e. each input maps to one and only one output) then you can theoretically compute for free (the Feynmann lectures on computation cover this well).
But these energies are negligible compared to the wattage that goes through a standard CPU.