From where do you know this ?

See: Quantum mechanics.

W.M.

The 2nd law is an empirical statement, based on observations like heat is never observed to flow spontaneously from a lower to a higher temperature.

No logics involved in that. Statistical physics has come a long way in explaining the 2nd law (including the increase of entropy in closed systems) on the basis of probabilistic arguments, but a full understanding, let alone a mathematical proof is still missing.

All sciences must abide by logical laws, and the second law of thermodynamics cannot be an exception. The second law of thermodynamics violates empirical principles.

Discontinuity (artificially) of The Thermophysical Properties of NIST affects the second law of thermodynamics：

1) Scientists create Type 2 perpetual motion machines;

2) Scientists have discovered new laws of phase transition.

3) Scientists don't need to create a bunch of fake things for the second law of thermodynamics.