Microscopic Irreversibility and the H Theorem
  Time-reversal had always been assumed to be a symmetry of physics at the fundamental level. In this paper we will explore the violations of time-reversal symmetry at the fundamental level and the consequences on thermodynamic systems. First, we will argue from from current physics that the universe dynamics is not time-reversal invariant. Second, we will argue that any thermodynamic system cannot be isolated from the rest of the universe. We then discuss how these two make the dynamics of thermodynamics systems very weakly irreversible at the classical and quantum level. Since time-reversal is no longer a symmetry of realistic systems, the problem of how macroscopic irreversibility arises from microscopic reversibility becomes irrelevant becomes there is no longer microscopic reversibility. At the classical level of thermodynamics system, we show that the H Theorem of Boltzmann is still valid even without microscopic reversibility. We do this by deriving a modified H Theorem, which still shows entropy monotonically increasing. At the quantum level, we show the the effect of CP violation, small irreversible changes on the internal states of the nuclear and atomic energy levels of thermodynamic systems. Thus, we remove Loschmidts's objection to Boltzmann's ideas. 
Jose A. Magpantay
cond-mat.stat-mech