Theory of Thermodynamic Measurements of Quantum Systems Far from Equilibrium

1. Front Matter

   Pages i-xvii

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2. Introduction

   • Abhay Shastry

   Pages 1-11

3. Temperature and Voltage

   • Abhay Shastry

   Pages 13-42

4. Coldest Measurable Temperature

   • Abhay Shastry

   Pages 43-59

5. STM as a Thermometer

   • Abhay Shastry

   Pages 61-75

6. Entropy

   • Abhay Shastry

   Pages 77-114

7. Concluding Remarks

   • Abhay Shastry

   Pages 115-117

8. Back Matter

   Pages 119-144

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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.

• nonequilibrium quantum thermodynamics
• Onsager matrix
• second law of thermodynamics
• local entropy in quantum system
• temperature in quantum system
• voltage in quantum system
• scanning probe microscopy
• temperature outside equilibrium

• Department of Chemistry, University of Toronto, Toronto, Canada

  Abhay Shastry

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.

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