The second law of thermodynamics as a deterministic theorem for quantum spin systems

We review our approach to the second law of thermodynamics as a theorem asserting growth mean (Gibbs–von Neumann) entropy quantum spin systems undergoing automorphic (unitary) adiabatic transformations. Non-automorphic interactions with environment, although known produce on average strict reduction finite number degrees freedom, are proved conserve average. The results depend crucially two properties entropy, by Robinson and Ruelle for classical Lanford lattice systems: upper semicontinuity affinity.