What if the second law of thermodynamics, in the hierarchy of physical laws, were at the same level as the fundamental laws of mechanics, such as the great conservation principles? What if entropy were an intrinsic property of matter at the same level as energy is universally understood to be? What if irreversibility were an intrinsic feature of the microscopic dynamical law of all physical objects, including an individual qubit or qudit?
This talk will show how positive answers to these questions need not contradict any of the known results of quantum mechanics. We construct a logically consistent, mathematically sound and definite, physically intriguing, non-relativistic and non-statistical quantum theory, in which the second law of thermodynamics is embedded as a fundamental microscopical law. The theory hinges upon a nonlinear extension of unitary Hamiltonian dynamics which for uncorrelated and noninteracting systems reduces to the usual Schroedinger equation for the zero entropy states, but in general generates a group (not a semi group) of irreversible time evolutions, where the non-Hamiltonian entropy generating term in the evolution equation attracts the state towards the direction of maximal entropy increase. Various examples and features of this highly non-conventional dynamical theory are discussed. References available at http://www.quantumthermodynamics.org/