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Entropy

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

Abstract

In this chapter, we shall discuss entropy in the context of the steady-state quantum transport problem. The work presented here deals with noninteracting fermions. We consider situations where we have a few reservoirs which exchange particles and energy with each other through a central scattering region. The distribution within the reservoirs, specified by their temperature and chemical potential, set the boundary conditions for the scattering problem. The scattering basis provides the most natural framework for the analysis of this problem. We derive the exact local entropy in the scattering basis and show that it is additive over subspaces of the one-body Hilbert space. We systematically develop the entropies that would be inferred by a local observer with access to varying degrees of information about the system. We prove inequalities connecting these entropy measures and find that the least knowledgeable formulation leads to the greatest entropy. We also prove statements of the third law of thermodynamics for open quantum systems in equilibrium and in nonequilibrium steady states. Finally, appropriately normalized (per-state) local entropies are defined and are used to quantify the departure from local equilibrium. We provide exact results in the absence of many-body interactions but only a working ansatz in their presence.

Keywords

Exact local entropy Entropy inferred from a local measurement Entropy inferred from a probe measurement Entropy inequalities Maximum entropy principle Entropy in the scattering basis von Neumann entropy Entanglement entropy Entropy matrix Subsystem entropy Total entropy Per-state entropy deficit Information Local distribution function Local density of states Fermi–Dirac distribution Scattering states Jensen’s inequality Concavity Third law of thermodynamics Localized states Open quantum system Benzene Pyrene Noninteracting Interacting Ansatz 

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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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