The only place in audio where a burn in of significant duration could have measurable differences are tubes and certain (very uncommon) loudspeaker drivers with a ceramic spider (like older Mark Audio drivers).
Tubes that are fresh (never used) react on the high voltage and heater and the components inside must settle, that can take a few hours to days and you can easely (if you hve a tube measurement device) measure the differences.
Ceramic spiders need to loosen up by tiny movements, that's why those speaker builders who use that kind of spiders (very rare) specify that. Older Mark Audio drivers are the most known drivers known for that. Some other drivers have similar spiders but don't specify that because the burn in happened at the factory (but the price is quiet high due to that). Mark Audio does not do that because they want to keep their drivers cheap. Their newer lines don't have that spider, and don't need that burn in anymore.