  Chemical potential is a property which involves the effect of interaction
between the components of a system, and it results from the whole system. In
this paper, we argue that for two particles which have interacted via their
spins and are now spatially separated, the so-called Bell's locality condition
implies that the chemical potential of each particle is an individual property.
Here is a point where quantum statistical mechanics and the local hidden
variable theories are in conflict. Based on two distinct concepts of chemical
potential, the two theories predict two different patterns for the energy
levels of a system of two entangled particles. In this manner, we show how one
can distinguish the non-separable features of a two-particle system.
