I read in the context of quantum computing or of the minimal energy required for computation that there has to be a minimum possible amount of energy required to change one bit of information, called the Landauer limit. During collapse of a wave function, for example for one of a pair of entangled particles, it seems one is losing information content (losing one bit as the wave function goes from either possible state to one). If so does this imply that collapse requires energy? Or is the Landuaer limit not relevant to this setting.
The collapse of the wavefunction is not a real physical process. It's a feature of a particular interpretation of quantum mechanics, the Copenhagen interpretation (CI). Other interpretations, such as the many-worlds interpretation (MWI), don't have such a collapse. The different interpretations make the same predictions about all observables, and therefore wavefunction collapse can't have any observable consequences, such as consumption of energy.
Perhaps not a real yes/no answer: Landauer principle is about something resembling the collapse of wave function, but deeply different: erasure of information such that it is indistinguishable from thermal noise. A collapse is not the same thing.
The following papers will perhaps be helpful:
Erasing the results of a quantum mechanical measurement has the cost in free energy required by Landauer's principle, see: