Partial entropy in finite-temperature phase transitions

It is shown that the von Neumann entropy, a measure of quantum entanglement, does have its classical counterpart in thermodynamic systems, which we call partial entropy. Close to the critical temperature, the partial entropy shows perfect finite-size scaling behavior even for quite small system sizes. This provides a powerful tool to quantify finite-temperature phase transitions as demonstrated on the classical Ising model on a square lattice and the ferromagnetic Heisenberg model on a cubic lattice.