Springer Theses

Theory of Thermodynamic Measurements of Quantum Systems Far from Equilibrium

Authors: Shastry, Abhay

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  • 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
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eBook $119.00
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  • ISBN 978-3-030-33574-8
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Hardcover $159.99
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  • ISBN 978-3-030-33573-1
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About this book

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.

About the authors

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.

Table of contents (6 chapters)

Table of contents (6 chapters)

Buy this book

eBook $119.00
price for USA in USD (gross)
  • ISBN 978-3-030-33574-8
  • Digitally watermarked, DRM-free
  • Included format: PDF, EPUB
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $159.99
price for USA in USD
  • ISBN 978-3-030-33573-1
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
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Bibliographic Information

Bibliographic Information
Book Title
Theory of Thermodynamic Measurements of Quantum Systems Far from Equilibrium
Authors
Series Title
Springer Theses
Copyright
2019
Publisher
Springer International Publishing
Copyright Holder
Springer Nature Switzerland AG
eBook ISBN
978-3-030-33574-8
DOI
10.1007/978-3-030-33574-8
Hardcover ISBN
978-3-030-33573-1
Series ISSN
2190-5053
Edition Number
1
Number of Pages
XVII, 144
Number of Illustrations
2 b/w illustrations, 22 illustrations in colour
Topics