Does "due compensation" apply to state "borrowing" of an asset?

If a police officer uses Posse Comitatus to borrow your vehicle for a chase, can you claim "rental value" from the state under the due compensation clause of the 5th amendment?
What about other situations where the state, rather than taking your property under eminent domain, "borrows" it and returns it later, possibly worse for wear?
Note this is a "United States" question, other nations' laws are different.
Asked Nov 12, 2015

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