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Experimentally, if object A is in equilibrium with object B, and object B is in equilibrium with object C, then object A is in equilibrium with object C. That statement of transitivity is called the "zeroth law of thermodynamics." For example, a cold metal block and a hot metal block are both placed on a metal plate at room temperature. Eventually, the cold block and the plate will be in thermal equilibrium. In addition, the hot block and the plate will be in thermal equilibrium.
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Thermodynamics of an Empty Box.

Georg J Schmitz1, Michael Te Vrugt2, Tore Haug-Warberg3

  • 1MICRESS Group, ACCESS e.V., Intzestr. 5, D-52072 Aachen, Germany.

Entropy (Basel, Switzerland)
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This study treats an empty box as a thermodynamic system, revealing its geometric degrees of freedom. This approach connects fundamental physics concepts like mechanics and relativity to thermodynamics.

Keywords:
Euler homogeneityLorentz factorToEUnruh temperatureanisotropic Hubble parameterblack-hole entropyclassical mechanicsquantized spacequantum mechanics

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Area of Science:

  • Thermodynamics
  • Statistical Mechanics
  • Theoretical Physics

Background:

  • The 'gas in a box' model is foundational in thermodynamics and statistical mechanics.
  • Existing research typically focuses on the gas, treating the box as mere confinement.
  • This work shifts focus to the box itself as the primary system of study.

Purpose of the Study:

  • To develop a thermodynamic theory centered on the geometric degrees of freedom of an empty box.
  • To explore the connections between the thermodynamics of an empty box and other areas of physics.

Main Methods:

  • Treating the geometric degrees of freedom of the box as thermodynamic degrees of freedom.
  • Applying standard mathematical methods to the thermodynamics of an empty box.
  • Deriving equations based on this novel thermodynamic framework.

Main Results:

  • Equations derived for the empty box exhibit structural similarities to those in cosmology, classical mechanics, and quantum mechanics.
  • The model system demonstrates unexpected links to classical mechanics, special relativity, and quantum field theory.
  • A new perspective on the thermodynamic properties of geometric confinement is established.

Conclusions:

  • The empty box, when treated thermodynamically, serves as a powerful and versatile model system.
  • This approach bridges thermodynamics with fundamental theories across classical and modern physics.
  • Geometric thermodynamics offers novel insights into the nature of physical systems and their interactions.