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Geometric Optimisation of Quantum Thermodynamic Processes.

Paolo Abiuso1, Harry J D Miller2, Martí Perarnau-Llobet3

  • 1ICFO-Institut de Ciències Fotòniques, The Barcelona Institute of Science and Technology, 08860 Castelldefels, Barcelona, Spain.

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This summary is machine-generated.

Differential geometry provides tools to optimize thermodynamic processes. This study introduces thermodynamic length and a quantum entropy production bound, offering new insights into finite-time thermodynamics.

Keywords:
coolingfinite-time thermodynamicsheat enginesquantum thermodynamicsthermodynamic length

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Area of Science:

  • Thermodynamics
  • Quantum Mechanics
  • Differential Geometry
  • Statistical Mechanics

Background:

  • Finite-time thermodynamic processes are crucial for understanding real-world systems.
  • Differential geometry offers a geometric perspective on thermodynamic state spaces.
  • Existing frameworks for quantum thermodynamics lack a unified geometric approach.

Purpose of the Study:

  • To introduce and explain the concept of thermodynamic length in classical and quantum regimes.
  • To present a quantum generalization of the geometric lower bound on finite-time entropy production.
  • To derive general principles for optimizing thermodynamic processes, particularly in the linear-response regime.

Main Methods:

  • Pedagogical introduction to thermodynamic length.
  • Review and connection of different quantum frameworks (adiabatic, Lindblad, discrete).
  • Derivation of a geometric lower bound on entropy production.
  • Analysis of optimization principles in the linear-response regime.

Main Results:

  • Established thermodynamic length as a key concept in quantum thermodynamics.
  • Presented a quantum geometric lower bound on entropy production.
  • Identified optimal strategies for finite-time thermodynamic processes, including constant control speed and specific conditions for Carnot engines.

Conclusions:

  • Differential geometry provides a powerful and unified framework for analyzing and optimizing thermodynamic processes.
  • The introduced quantum entropy production bound offers new theoretical limits for thermodynamic efficiency.
  • The derived optimization principles pave the way for designing more efficient classical and quantum engines and refrigerators.