### 2.4 Entropy of a system of finite size at finite temperature

In a more general situation one starts with a system of finite size in a mixed thermal state at
temperature . This system is divided by the entangling surface in two sub-systems of characteristic
size . Then, the entanglement entropy is a function of several parameters (if the field in question is
massive then mass should be added to the parameters on which the entropy should depend)
where is a UV cut-off. Clearly, the entanglement entropy in this general case is due to a combination of
different factors: the entanglement between two sub-systems and the thermal nature of the initial mixed
state. In dimensions even for simple geometries this function of 4 variables is not known explicitly.
However, in two spacetime dimensions, in some particular cases, the explicit form of this function is
known.