Thermodynamics of an Empty Box

Abstract

A gas in a box is perhaps the most important model system studied in thermodynamics and statistical mechanics. Usually, studies focus on the gas, whereas the box merely serves as an idealized confinement. The present article focuses on the box as the central object and develops a thermodynamic theory by treating the geometric degrees of freedom of the box as the degrees of freedom of a thermodynamic system. Applying standard mathematical methods to the thermodynamics of an empty box allows equations with the same structure as those of cosmology and classical and quantum mechanics to be derived. The simple model system of an empty box is shown to have interesting connections to classical mechanics, special relativity, and quantum field theory.

References in corpus (19)

• On the Origin of Gravity and the Laws of Newton
• The Unruh effect and its applications
• Dimensional Reduction in Quantum Gravity
• Bianchi type III models with anisotropic dark energy
• Is there proof that backreaction of inhomogeneities is irrelevant in cosmology?
• Testing backreaction effects with observations
• Theory of Cross Phenomena and Their Coefficients Beyond Onsager Theorem
• Noether's Theorem in Statistical Mechanics
• Mori-Zwanzig projection operator formalism for systems with time-dependent Hamiltonians
• Projection operators in statistical mechanics: a pedagogical approach
• From a microscopic inertial active matter model to the Schrödinger equation
• Why Noether's Theorem applies to Statistical Mechanics
• Why is the Temperature of the Universe 2.726K?
• The Science of $\Theta {\Delta }^{cs}$
• An Anisotropic Model for the Universe
• A Note on the Entropy Force in Kinetic Theory and Black Holes
• Is thermodynamics fundamental?
• Alpha and Electro-weak Coupling
• Entropy Dynamics of Phonon Quantum States Generated by Optical Excitation of a Two-Level System