In the third law of thermodynamics, entropy goes to zero or to a constant value at vanishing absolute temperature. The change of entropy also goes to zero.
The third law is valid in the thermodynamic limit, which means, it is valid in the case that the system is infinitely large. In contrast, in the real world, systems are of finite size.
Is entropy continuous in real life, when systems have finite size? And is the third law of thermodynamics correct for finite systems?
EDIT: What happens for nanoparticles with 10, 100, 1000 or 10000 atoms?