Ken Liu's chilling short story "The Message" [0] explores what this might look like on the receiving end.
[0]: https://archive.org/details/interzone-magazine-242-2012-09-1...
[0]: https://archive.org/details/interzone-magazine-242-2012-09-1...
If nothing else they appear to have microelectronics (e.g. video playback and displays). Manufacture of that requires knowledge of radiation because you need to keep the encapsulation material low-activity. Plus the general ideas behind semiconductors and microlithography are based on physics very close to the physics of ionising radiation (e.g. photoelectric effect) and you probably use D/EUV, X-rays and ion/electron beams somewhere in the process too.
The entropy arrow definition would have worked here.