It is argued that certain recent advances in the construction of a theory of the collapses of Quantum Mechanical wave functions suggest the possibility of new and improved foundations for statistical mechanics, foundations in which epistemic considerations play no role.
Statistical mechanics is often taken to be the paradigm of a successful inter-theoretic reduction, which explains the high-level phenomena by using the fundamental theories of physics together with some auxiliary hypotheses. The central idea of statistical mechanics is that in order to account for the thermodynamic regularities only partial information about the microstates is needed, concerning some macrovariables of them, that is, concerning the fact that they belong to certain macrostates in which all the microstates share the same macrovariables. An important example of a thermodynamic property, which needs to be explained in quantum statistical mechanics, is that of being in thermal equilibrium. The thermodynamic law of approach to equilibrium says that systems, prepared in non-equilibrium states, will invariably evolve to equilibrium states fixed by the constraints on these systems, and remain in them indefinitely.
Questions about the route from a nonequilibrium initial state to the final global equilibrium have played an important role since the early days of phenomenological thermodynamics and statistical mechanics. Nowadays, their implications reach from central technical devices of the contemporary human society, like heat engines, refrigerators and computers to recent physics at almost all length scales, from Bose-Einstein-condensation and superconductors to black holes. This work addresses the foundation of macroscopic laws concerning the decay to equilibrium, e.g. the celebrated Fourier's Law, on microscopic Schrödingerian quantum dynamics. Here, a proper treatment requires the usage of modern methods in theoretical physics such as the Theory of Open Quantum Systems, the Kubo Formula in Liouville Space and the novel Hilbert Space Average Method. It turns out that both the relaxation to equilibrium as well as the transport of heat is mainly determined by quantum effects comparable to the role of entanglement in considerations of the global equilibrium within Quantum Thermodynamics. Finally, the foundation of phenomenological thermodynamics on a microscopic theory will hopefully improve our understanding of those most impressive and far-reaching theories and their background and will possibly open the way to overcoming their nanoscopic limits.
Entropy Beyond the Second Law presents a coherent formulation of all aspects of thermodynamics and statistical mechanics with entropy as the unifying theme. This includes formulating equilibrium theory and explaining the role of the Second Law in establishing the equilibrium state. It also establishes the foundations of non-equilibrium theory by generalizing the concept of entropy in an appropriate way. Finally, it addresses the relationship between classical and quantum statistical mechanics by invoking the collapse of the wave function into entropy states. A secondary purpose is to increase the understanding of entropy and the Second Law, and to correct misapprehensions and errors that have arisen over the years.