A Schrödinger-like equation for the Thermodynamics of a particle in a box

• URL: http://arxiv.org/abs/2603.28820v1
• Date: Sun, 29 Mar 2026 01:00:26 GMT
• Title: A Schrödinger-like equation for the Thermodynamics of a particle in a box
• Abstract summary: An expanding/contracting 1-dimension box is revisited in action-angle like variables with direct thermodynamic interpretation.<n>Heat transfer at constant volume is analyzed, and the derived thermal conductance matches the universal quantum of heat conductance $G_Q$ in the quantum limit.
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• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: The particle in an expanding/contracting 1-dimension box is revisited in action-angle like variables with direct thermodynamic interpretation. An angle dependent potential is proposed accurately describing the mechanical behavior while also capturing thermodynamic evolution -- entropy production -- within a canonical Hamiltonian framework. Heat transfer at constant volume is analyzed, and the derived thermal conductance matches the universal quantum of heat conductance $G_{Q}$ in the quantum limit. Having a Hamiltonian scheme interpretable in thermodynamic terms, a Schrödinger-like wave equation is formulated whose wavefunction solutions contain the information about the entropy evolution. The results show exact agreement with 'classical' results for non abrupt changes. Finally, comparisons with a pure quantum mechanical treatment of the wave function in an expanding box confirm consistency in quasi-static regimes and reveal adiabaticity breakdown under far-from-equilibrium conditions.

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