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Updated: Jun 20, 2026
11:03
An Analog Macroscopic Technique for Studying Molecular Hydrodynamic Processes in Dense Gases and Liquids
Published on: December 4, 2017
Canonical quantization for equilibrium thermodynamics
Luis F Santos1, Victor Hugo M Ramos1, Danilo Cius1
1University of São Paulo, Department of Mathematical Physics, Institute of Physics, Rua do Matão 1371, São Paulo 05508-090, São Paulo, Brazil.
Physical Review. E
|June 19, 2026
Summary
This study introduces a quantum framework for thermodynamics using constrained systems. It reveals an entropy-time Schrödinger equation and thermodynamic uncertainty relations for gases.
Area of Science:
- Thermodynamics
- Quantum Mechanics
- Statistical Mechanics
Background:
- Traditional thermodynamics lacks a rigorous quantum mechanical foundation.
- Dirac's theory of constrained systems offers a potential framework for quantizing thermodynamic variables.
Purpose of the Study:
- To formulate a canonical quantization of equilibrium thermodynamics.
- To apply this formalism to various gas models and explore its implications.
Main Methods:
- Application of Dirac's theory of constrained systems to thermodynamic variables.
- Treating thermodynamic variables as conjugate operators in a Hilbert space.
- Illustrating quantization procedures for ideal, van der Waals, and photon gases.
Main Results:
- Development of a quantum formalism for thermodynamics.
- Emergence of a Schrödinger-like equation for the ideal gas with entropy as time.
- Establishment of thermodynamic uncertainty relations.
- Demonstration of pseudo-Hermitian framework for operator Hermiticity.
Conclusions:
- The proposed quantum framework provides a novel perspective on equilibrium thermodynamics.
- The formalism naturally yields thermodynamic uncertainty relations.
- Suggests potential extensions to quantum phase transitions, black hole thermodynamics, and nonequilibrium systems.
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