To the best of my knowledge, fiat currency is legally defined as being fungible, but since it has serial numbers, I recently saw an article that was talking about how Germany was putting serial number readers into like ATMs and banks so they could track the flow of fiat currency even in physical form by reading the serial numbers.

At least as far as knowing that it came out of this bank in this one town and went into a different bank in this other town, say halfway across the country, and maybe even put serial number readers in store cash registers so that you can see which stores it went through.