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Nonextensive thermodynamic functions in the Schrödinger-Gibbs ensemble
J L Alonso1,2,3, A Castro4, J Clemente-Gallardo1,2,3
1Departamento de Física Teórica, Universidad de Zaragoza, Pedro Cerbuna 12, 50009 Zaragoza, Spain.
Summary
This study shows that a specific quantum thermodynamics model, inspired by Schrödinger, fails for composite systems. It demonstrates that this model cannot define essential thermodynamic properties like free energy, making it unsuitable for quantum equilibrium thermodynamics.
Area of Science:
- Quantum Mechanics
- Statistical Thermodynamics
- Quantum Information Theory
Background:
- Schrödinger questioned basing thermodynamics solely on quantum eigenstates.
- Interpretations involve density distributions on quantum pure states weighted by Hamiltonian expectation values.
Purpose of the Study:
- To analyze a specific density distribution for composite quantum systems.
- To determine if this distribution yields factorizable partition functions and extensive thermodynamic properties.
Main Methods:
- Focus on a well-known density distribution inspired by Schrödinger's idea.
- Analysis of partition functions in composite quantum systems.
- Investigation of thermodynamic magnitudes in the thermodynamical regime.
Main Results:
- The partition functions defined by the distribution do not factorize for composite systems.
- This non-factorization persists even in the thermodynamical regime.
- Extensive thermodynamic magnitudes (free energy, internal energy, entropy) cannot be defined.
Conclusions:
- The analyzed distribution, inspired by Schrödinger, is inappropriate for constructing quantum equilibrium thermodynamics.
- The model's failure in composite systems highlights limitations in applying certain quantum statistical approaches.
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