We study the $p$-adic behaviour of multiplicative Euler characteristics for sequences of groups. Under suitable conditions a renormalized limit exists and equals a $p$-adic analogue of the Li - Thom R-torsion, which they introduced for the purpose of entropy calculations.
Links:
[1] https://www.mpim-bonn.mpg.de/de/taxonomy/term/39
[2] https://www.mpim-bonn.mpg.de/de/node/3444
[3] https://www.mpim-bonn.mpg.de/de/node/7800