Searching for quantum non-thermodynamic phenomena

Abstract: Recent research on the fundamentals of statistical mechanics has led to an interesting discovery [1-3]: With locally nonchaotic barriers, as Boltzmann's H-theorem is inapplicable, there exist nontrivial non-thermodynamic systems that can produce useful work by absorbing heat from a single thermal reservoir without any other effect, thereby breaking the boundaries of the second law of thermodynamics. The previous analyses used classical mechanical models. In the current investigation, the study is extended to quantum mechanics. First, we reiterate that the Fermi-Dirac distribution and the Bose-Einstein distribution are compatible with the generalized Maxwell's relations, which demonstrates the general robustness of the framework of quantum statistical mechanics. Next, we analyze a set of simple-step scattering problems. When the system is in contact with a thermal reservoir, a bound state inherently follows the second law of thermodynamics, while a scattering state may not. The root cause is associated with the nonlocal nature of the wave function. It implies that the non-thermodynamic phenomena favor unquantized energy and localized wave packets, exhibiting a tendency to occur in "semiclassical" setups.