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Introduction

  • Abhay Shastry
Chapter
Part of the Springer Theses book series (Springer Theses)

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 book 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 is discussed and particular attention is paid to the second and third laws. A detailed discussion of what constitutes an ideal measurement is also included. 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. Proofs of the third law of thermodynamics are given for open quantum systems in equilibrium and in nonequilibrium steady states. We provide exact results pertaining to the entropy in the absence of many-body interactions but a working ansatz in their presence.

Keywords

Local equilibrium hypothesis Thermal equilibrium Nonequilibrium steady state Nonequilibrium green’s functions Temperature Chemical potential (also voltage) Quantum fermion system Reversible thermodynamics Irreversible thermodynamics Laws of thermodynamics Zeroth Second and third laws of thermodynamics Onsager statement of the second law of thermodynamics Scanning tunneling thermometer Single-molecular junction Atomic-size contact junction Entropy Meir–Wingreen formula Bergfield–Stafford formula 

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Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  • Abhay Shastry
    • 1
  1. 1.Department of ChemistryUniversity of TorontoTorontoCanada

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