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Thermodynamic potentials are state functions that are extremely useful in analyzing a thermodynamic system. They have dimensions of energy. The four important thermodynamic potentials are internal energy, enthalpy, Helmholtz free energy, and Gibbs free energy. These thermodynamic potentials can be expressed using two of the following variables: pressure, volume, temperature, and entropy. These two variables are expressed as the rate of change of the thermodynamic potential with respect to other...
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A thermodynamic system is a set of objects whose thermodynamic properties are of interest. The system is considered to be embedded in its surroundings or the environment. The system and its environment can exchange heat and do work on each other through a boundary that separates them. However, the immediate surroundings of the system interact with it directly and therefore have a much stronger influence on its behavior and properties.
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Quantum Thermodynamics at Strong Coupling: Operator Thermodynamic Functions and Relations.

Jen-Tsung Hsiang1, Bei-Lok Hu2

  • 1Center for Field Theory and Particle Physics, Department of Physics, Fudan University, Shanghai 200433, China.

Entropy (Basel, Switzerland)
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Summary

This study explores quantum thermodynamics, focusing on small quantum systems strongly coupled to heat baths. It reexamines thermodynamic laws and functions for quantum systems, addressing challenges in energy and entropy definitions.

Keywords:
operator thermodynamic functionsquantum thermodynamicsstrong coupling

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Area of Science:

  • Physics
  • Quantum Mechanics
  • Thermodynamics

Background:

  • Emergence in physical sciences, particularly thermodynamics, offers insights into complex systems.
  • Traditional thermodynamics, based on large, weakly coupled systems, has limitations when applied to quantum phenomena.
  • Understanding quantum mechanics as an emergent theory necessitates a robust framework for quantum thermodynamics.

Purpose of the Study:

  • To establish the foundations of quantum thermodynamics for small quantum many-body systems.
  • To address new issues and formulate rules for quantum systems strongly coupled to heat baths.
  • To reexamine the meaning, viability, and validity of thermodynamic functions, relations, and laws in the quantum regime.

Main Methods:

  • Overview of quantum formulations based on Gelin & Thoss and Seifert.
  • Quantum formulation of Jarzynski's two representations.
  • Construction of operator thermodynamic potentials and verification of their relations.

Main Results:

  • Identified challenges in defining thermodynamic functions for quantum systems, especially at strong coupling.
  • Demonstrated the construction of operator thermodynamic potentials yielding familiar thermodynamic variables.
  • Highlighted subtleties in energy and entropy definitions and their operator forms in quantum thermodynamics.

Conclusions:

  • Establishing a viable quantum thermodynamics requires constructing and verifying operator thermodynamic functions and their relations.
  • Strong coupling in quantum systems introduces complexities not present in traditional thermodynamics.
  • Further research is needed to develop a comprehensive theory of quantum thermodynamics.