Theory of Thermodynamic Measurements of Quantum Systems Far From Equilibrium

Abstract

Thermodynamics is a well established field which studies systems in equilibrium and provides some of the most general results in all of physics. Unluckily, the vast majority of systems encountered in Nature are out of equilibrium. Thermodynamic descriptions of nonequilibrium systems are a formidable theoretical challenge and most results have been obtained under the assumption of a local equilibrium. Outside such an assumption, definitions of basic thermodynamic state variables such as temperature and voltage are muddled with a competing panoply of ``operational"" definitions. The work presented in this thesis provides a mathematically rigorous foundation for temperature and voltage measurements in quantum systems far from equilibrium. We show the existence and uniqueness of temperature and voltage measurements for any quantum fermion system in a steady-state, arbitrarily far from equilibrium, and with arbitrary interactions within the quantum system. We show that the uniqueness of these measurements is intimately tied to the second law of thermodynamics. In achieving this goal, we prove the positive-definiteness of the Onsager matrix in the context of thermoelectric transport which had only been a phenomenological statement for the past 85 years. The validity of the laws of thermodynamics far from equilibrium are discussed in detail. These results have fundamental implications for the field of scanning probe microscopy. We propose a method for imaging temperature fields in nanoscopic quantum conductors where we anticipate a remarkable improvement in the spatial resolution by over two orders of magnitude. Finally, we discuss the entropy of a quantum system far from equilibrium. We obtain a hierarchy of inequalities for the entropy of the quantum system and discuss its intimate relation to the information available from a measurement. We provide exact results pertaining to the entropy in the absence of many-body interactions but a working ansatz in their presence.