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Calculation of First-Law Quantities II01:24

Calculation of First-Law Quantities II

The first law of thermodynamics establishes that the change in internal energy of a system is given by ΔU = q + w, where q is the heat exchanged, and w is the work performed. For a perfect gas, both internal energy (U) and enthalpy (H) depend solely on temperature. Consequently, for any change of state, whether reversible or irreversible, the internal energy change is determined by integrating the heat capacity at constant volume, and the enthalpy change by integrating the heat capacity at...
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Ludwig Edward Boltzmann developed a definition for entropy, which stated that absolute entropy is proportional to the natural logarithm of the number of possible combinations of particles. Entropy stands alone among state functions as the only one whose absolute values can be determined.Consider a gas sample confined to a container. As the container expands, the energy levels of gas molecules become more closely spaced. This increases the number of available energy states, thereby increasing...
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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
PubMed
Summary
This summary is machine-generated.

This study introduces a quantum framework for thermodynamics using constrained systems. It reveals an entropy-time Schrödinger equation and thermodynamic uncertainty relations for gases.

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Generation and Coherent Control of Pulsed Quantum Frequency Combs
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Generation and Coherent Control of Pulsed Quantum Frequency Combs

Published on: June 8, 2018

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Last Updated: Jun 20, 2026

An Analog Macroscopic Technique for Studying Molecular Hydrodynamic Processes in Dense Gases and Liquids
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Published on: December 4, 2017

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Generation and Coherent Control of Pulsed Quantum Frequency Combs

Published on: June 8, 2018

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.