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Heat and temperature are essential concepts for everyone every day. The study of heat and temperature is part of an area of physics known as thermodynamics. It is not always easy to distinguish heat and temperature.
The concept of temperature has evolved from the common concepts of hot and cold. The scientific definition of temperature explains more than just our sense of hot and cold. Temperature is operationally defined as the quantity measured with a thermometer. Furthermore, temperature is...
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A reversible chemical reaction represents a chemical process that proceeds in both forward (left to right) and reverse (right to left) directions. When the rates of the forward and reverse reactions are equal, the concentrations of the reactant and product species remain constant over time and the system is at equilibrium. A special double arrow is used to emphasize the reversible nature of the reaction. The relative concentrations of reactants and products in equilibrium systems vary greatly;...
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The free energy change for a process may be viewed as a measure of its driving force. A negative value for ΔG represents a driving force for the process in the forward direction, while a positive value represents a driving force for the process in the reverse direction. When ΔGrxn is zero, the forward and reverse driving forces are equal, and the process occurs in both directions at the same rate (the system is at equilibrium).
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Solution Equilibrium and Saturation01:59

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Imagine adding a small amount of sugar to a glass of water, stirring until all the sugar has dissolved, and then adding a bit more. You can repeat this process until the sugar concentration of the solution reaches its natural limit, a limit determined primarily by the relative strengths of the solute-solute, solute-solvent, and solvent-solvent attractive forces. You can be certain that you have reached this limit because, no matter how long you stir the solution, undissolved sugar remains. The...
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Updated: Feb 13, 2026

Non-equilibrium Microwave Plasma for Efficient High Temperature Chemistry
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Entropic bounds between two thermal equilibrium states.

Julio A López-Saldívar1,2, Octavio Castaños1, Margarita A Man'ko3

  • 1Instituto de Ciencias Nucleares, Universidad Nacional Autónoma de Mexico, Apdo. Postal 70-543, 04510, CDMX, Mexico.

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Summary

Positivity conditions of relative entropy provide bounds for thermodynamic potentials between thermal equilibrium states. These bounds apply to molecules, qubits, and harmonic oscillators, using system Hamiltonians and temperatures.

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Area of Science:

  • Thermodynamics
  • Quantum Information Theory
  • Statistical Mechanics

Background:

  • Relative entropy quantifies distinguishability between quantum states.
  • Thermodynamic potentials (entropy, Helmholtz, Gibbs) are crucial in characterizing systems at thermal equilibrium.

Purpose of the Study:

  • To derive upper and lower bounds for differences in thermodynamic potentials between two thermal equilibrium states.
  • To explore the applicability of these bounds to various quantum systems.

Main Methods:

  • Utilizing the positivity conditions of relative entropy.
  • Expressing bounds in terms of mean values of Hamiltonians, number operators, and temperatures.
  • Applying the formalism to molecular systems (Franck-Condon coefficients), general qubit systems, and harmonic oscillators.

Main Results:

  • Established bounds for the subtraction of entropies, Helmholtz, and Gibbs potentials.
  • Demonstrated the dependence of these bounds on system parameters like mean energy and temperature.
  • Showcased specific applications for time-dependent Hamiltonians and Franck-Condon factors.

Conclusions:

  • The derived bounds offer a way to constrain thermodynamic quantities using relative entropy.
  • The results are generalizable across different quantum systems, including those with time-varying properties.