Theory of Thermodynamic Measurements of Quantum Systems Far from Equilibrium

This thesis presents several related advances in the field of nonequilibrium quantum thermodynamics. The central result is an ingenious proof that the local temperature and voltage measurement in a nonequilibrium system of fermions exists and is unique, placing the concept of local temperature on a rigorous mathematical footing for the first time. As an intermediate step, a proof of the positivity of the Onsager matrix of linear response theory is given -- a statement of the second law of thermodynamics that had lacked an independent proof for 85 years. A new experimental method to measure the local temperature of an electron system using purely electrical techniques is also proposed, which could enable improvements to the spatial resolution of thermometry by several orders of magnitude. Finally, a new mathematically-exact definition for the local entropy of a quantum system in a nonequilibrium steady state is derived. Several different measures of the local entropy are discussed, relating to the thermodynamics of processes that a local observer with varying degrees of information about the microstates of the system could carry out, and it is shown that they satisfy a hierarchy of inequalities. Proofs of the third law of thermodynamics for generic open quantum systems are presented, taking into account the entropic contribution due to localized states. Appropriately normalized (per-state) local entropies are defined and are used to quantify the departure from local equilibrium.

Nominated as an outstanding PhD thesis by the University of Arizona Discusses in detail the validity of the laws of thermodynamics far from equilibrium Presents a novel, mathematically-rigorous foundation for temperature and voltage measurements in far-from-equilibrium quantum systems Proves the positivity of the Onsager matrix for quantum thermoelectric transport, verifying a formulation of the second law of thermodynamics Based on the theoretical foundations developed here, the Scanning Tunneling Thermometer is proposed which may potentially improve the resolution of nanoscopic thermometry by over two orders of magnitude Derives the exact local entropy for nonequilibrium steady states, explores the second and third laws of thermodynamics, and proposes a metric to quantify the departure from local equilibrium

Autorentext
Abhay Shastry is a postdoctoral researcher in the Department of Chemistry at the University of Toronto. He received his PhD from the University of Arizona in 2018.

Inhalt
Chapter1. Introduction.- Chapter2. Temperature and Voltage.- Chapter3. Coldest Measurable Temperature.- Chapter4. STM as a Thermometer.- Chapter5. Entropy.- Chapter6. Concluding Remarks. <p