Thermodynamics of an Empty Box
Abstract
:1. Introduction
1.1. Scope
1.2. Outline
2. Thermodynamics
2.1. Mathematical Thermodynamics
Thermodynamic Potentials
2.2. Scalar Potentials, Gradients, and Forces
2.3. The Internal Energy of an Empty Box
Entropy—More than Statistics
3. Chopping the Box—Quantization of Space
- bulk voxels,
- face voxels,
- edge voxels,
- vertex voxels.
4. Applications of the Quantized Box Model
4.1. Thermodynamics of Geometric Objects
4.2. Dimensionless Entities
4.3. Squeezing the Box
Special Relativity
4.4. Evolution of the Box
4.5. Translating the Box
4.5.1. Newton’s Laws
4.5.2. The Unruh Effect
4.5.3. Position-Dependent Volume
4.5.4. Uncertainty Relation
5. Beyond the Empty Box
- all three laws of Newton (classical mechanics),
- the harmonic oscillator equation,
- the Unruh equation,
- an uncertainty relation.
5.1. Oriented Surfaces
5.2. Shearing and Twisting the Box
5.3. Filling the Box
6. Summary and Outlook
Author Contributions
Funding
Institutional Review Board Statement
Data Availability Statement
Conflicts of Interest
Appendix A. Legendre Transformations
Appendix B. Relation between Dual-State Entropy and Boltzmann Entropy
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Schmitz, G.J.; te Vrugt, M.; Haug-Warberg, T.; Ellingsen, L.; Needham, P.; Wittkowski, R. Thermodynamics of an Empty Box. Entropy 2023, 25, 315. https://doi.org/10.3390/e25020315
Schmitz GJ, te Vrugt M, Haug-Warberg T, Ellingsen L, Needham P, Wittkowski R. Thermodynamics of an Empty Box. Entropy. 2023; 25(2):315. https://doi.org/10.3390/e25020315
Chicago/Turabian StyleSchmitz, Georg J., Michael te Vrugt, Tore Haug-Warberg, Lodin Ellingsen, Paul Needham, and Raphael Wittkowski. 2023. "Thermodynamics of an Empty Box" Entropy 25, no. 2: 315. https://doi.org/10.3390/e25020315