This question was asked quite some time ago, but in the long drawn process of trying to get my head around irreversibility, I came across an article on the minus first law.
The minus first law is not a statement about energy. That energy cannot be created or destroyed is the content of the first law of thermodynamics. The minus first law is a statement of the empirically observed fact that an isolated system if left alone will spontaneously approach a unique state of equilibrium, see H. R. Brown and J. Uffink in their article, “The origins of time-asymmetry in thermodynamics: The minus first law”, published in 2001 in Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics Vol 32, p525.
That this state of affairs is found to arise in the natural world is the basic reason why there is a science of thermodynamics.
The authors point out that the minus first law is logically prior to the second law. The minus first law tells us that an isolated system prepared in a non-equilibrium state will approach equilibrium, the second law tells us that the entropy of this system will increase as a result, it does not tell us that the system will be driven towards equilibrium.
The physical underpinnings of the minus first law is another question entirely. I believe it is covered in one of Susskind's lectures in the classical case, making use of the ideas of dynamical chaos and coarse-graining. The quantum version is a different matter, the leading candidate as far as I know goes by the name of the eigenstate thermalisation hypothesis which can be readily found on Wikipedia.