Flow of Entropy in Equilibrium and Non-Equilibrium Quantum Systems

Abstract

This dissertation explores the flow of entropy, one of the most fundamental quantities in the physical sciences, as well as processes involved in the interconversion of entropy into electrical work and the converse, in a range of systems that define the current and coming technological revolution, those of open quantum systems in and out of equilibrium. Simple and comprehensible formulas for global and local heat and entropy currents are proposed and interpreted through the use of Non-Equilibrium Green's Function theory (NEGF). Thorough exploration and verification of the self-consistency of these formulas and their interpretation is made. An analysis of Joule heating in an exactly solvable model of a quantum wire is performed using the proposed unitary formula. It is shown that when very many local measurements are made of the nonequilibrium electron distribution in the wire, Joule heating, a fundamental electrical manifestation of the 2nd Law of Thermodynamics, is recovered. Linear thermoelectric coefficients of three-terminal quantum systems are defined and compared with their two-terminal analogs, leading to new thermodynamic relations previously unaccounted for. The role of topological fields and the persistent currents they generate in open quantum systems is discussed and reinterpreted, leading to the resolution of a thermodynamic paradox and the definition of a persistent-current analog of the Peltier coefficient. A generalization of the Peierls' substitution is presented, which permits the evaluation of local observables in the presence of magnetic fields. The conventional and proposed unitary descriptions of heat and entropy flow profiles in experimentally relevant models, such as carbon nanosheet segments, are contrasted and discussed.