This might be well known, but why's that? I've recently seen a Go implementation of LRU and it uses a lot of memory. Maybe this would allow us to save some of that in a better implementation.
The implementation in software was probably fully associative, i.e. every item can be cached in every slot. This requires a lot more memory and it is the same for caches in processors, they require more additional bits and logic the more freedom they have where to cache the content of every address.
To be more precise, you have to keep track of the order all cache entries were accessed which requires at least about n * log(n) bits unless you only implicitly store the access order by using something like move to front.