According to Landauer’s principle, there is energy cost for any exchange of information. Consequently, synchronization of clocks (and in general the introduction of a frame of reference) is an action that itself requires energy. This is often overlooked, and people think that frames of reference and coordinate systems exists in this ideal Platonic world.
This matter is the focus of the new paper:
Bormashenko, E.; Nosonovsky, M. Landauer Principle and Einstein Synchronization of Clocks: Ramsey Approach. Entropy 2025, 27, 697. https://doi.org/10.3390/e27070697