Second law of classical and quantum thermodynamics and its validity for any timescale and system size

Abstract

We develop a strategy to properly analyse the entropy in a classical system originally envisaged by Maxwell and extended it to quantum systems (molten liquid and water interacting with photons). We exploit the renormalized interaction to evaluate the entropy-change in these systems and have unequivocally identified the following two assumptions to be physically false. The false assumptions are related to (1) time reversibility and (2) reversible physical interaction(s) without any other changes. The second law of thermodynamics is found to be valid for any timescale and system size for as long as these two assumptions are violated, and stay violated. In the presence of any phase transition, or for larger systems with longer timescales, these two assumptions are automatically false. We prove that if we activate these assumptions at certain timescale and size, we are then led to the violation of the second law of thermodynamics.