We show how to measure the order-two Renyi entropy of many-body states of
spinful fermionic atoms in an optical lattice in equilibrium and
non-equilibrium situations. The proposed scheme relies on the possibility to
produce and couple two copies of the state under investigation, and to measure
the occupation number in a site- and spin-resolved manner, e.g. with a quantum
gas microscope. Such a protocol opens the possibility to measure entanglement
and test a number of theoretical predictions, such as area laws and their
corrections. As an illustration we discuss the interplay between thermal and
entanglement entropy for a one dimensional Fermi-Hubbard model at finite
temperature, and its possible measurement in an experiment using the present
scheme
