Heat Capacity as A Witness of Entanglement

We demonstrate that the presence of entanglement in macroscopic bodies (e.g. solids) in thermodynamical equilibrium could be revealed by measuring heat-capacity. The idea is that if the system were in a separable state, then for certain Hamiltonians heat capacity would not tend asymptotically to zero as the temperature approaches absolute zero. Since this would contradict the third law of thermodynamics, one concludes that the system must contain entanglement. The separable bounds are obtained by minimization of the heat capacity over separable states and using its universal low-temperature behavior. Our results open up a possibility to use standard experimental techniques of solid state physics -- namely, heat capacity measurements -- to detect entanglement in macroscopic samples.