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Related Concept Videos

Entropy Change in Reversible Processes01:10

Entropy Change in Reversible Processes

3.0K
In the Carnot engine, which achieves the maximum efficiency between two reservoirs of fixed temperatures, the total change in entropy is zero. The observation can be generalized by considering any reversible cyclic process consisting of many Carnot cycles. Thus, it can be stated that the total entropy change of any ideal reversible cycle is zero.
The statement can be further generalized to prove that entropy is a state function. Take a cyclic process between any two points on a p-V diagram.
3.0K
Phase Transitions02:31

Phase Transitions

21.6K
Whether solid, liquid, or gas, a substance's state depends on the order and arrangement of its particles (atoms, molecules, or ions). Particles in the solid pack closely together, generally in a pattern. The particles vibrate about their fixed positions but do not move or squeeze past their neighbors. In liquids, although the particles are closely spaced, they are randomly arranged. The position of the particles are not fixed—that is, they are free to move past their neighbors to...
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Entropy and the Second Law of Thermodynamics01:20

Entropy and the Second Law of Thermodynamics

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The second law of thermodynamics can be stated quantitatively using the concept of entropy. Entropy is the measure of disorder of the system.
The relation  between entropy and disorder can be illustrated with the example of the phase change of ice to water. In ice, the molecules are located at specific sites giving a solid state, whereas, in a liquid form, these molecules are much freer to move. The molecular arrangement has therefore become more randomized. Although the change in average...
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Entropy02:39

Entropy

33.0K
Salt particles that have dissolved in water never spontaneously come back together in solution to reform solid particles. Moreover, a gas that has expanded in a vacuum remains dispersed and never spontaneously reassembles. The unidirectional nature of these phenomena is the result of a thermodynamic state function called entropy (S). Entropy is the measure of the extent to which the energy is dispersed throughout a system, or in other words, it is proportional to the degree of disorder of a...
33.0K
Entropy01:18

Entropy

3.2K
The first law of thermodynamics is quantitatively formulated via an equation relating the internal energy of a system, the heat exchanged by it, and the work done on it. A quantitative formulation of the second law of thermodynamics leads to defining a state function, the entropy.
When an ideal gas expands isothermally, the disorder in the gas increases. From the molecular perspective, the gas molecules have more volume to move around in.
Consider an infinitesimal step in the expansion, which...
3.2K
Standard Entropy Change for a Reaction03:00

Standard Entropy Change for a Reaction

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Entropy is a state function, so the standard entropy change for a chemical reaction (ΔS°rxn) can be calculated from the difference in standard entropy between the products and the reactants.
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Related Experiment Video

Updated: Nov 15, 2025

Unraveling Entropic Rate Acceleration Induced by Solvent Dynamics in Membrane Enzymes
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Entropy Pair Functional Theory: Direct Entropy Evaluation Spanning Phase Transitions.

Donald M Nicholson1, C Y Gao2, Marshall T McDonnell2

  • 1Department of Physics and Astronomy, University of North Carolina, Asheville, NC 28803, USA.

Entropy (Basel, Switzerland)
|March 6, 2021
PubMed
Summary
This summary is machine-generated.

Excess entropy is a universal, temperature-independent functional of density and pair correlation functions for pair potentials. This simplifies free energy calculations from simulations, avoiding temperature-dependent thermodynamic integration.

Keywords:
entropyentropy functionalfree energypair correlation functionpair distribution function

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Area of Science:

  • Statistical Mechanics
  • Computational Chemistry
  • Condensed Matter Physics

Background:

  • Henderson's theorem establishes free energy as a temperature-dependent functional.
  • Existing methods for free energy calculation often require thermodynamic integration.

Purpose of the Study:

  • To prove excess entropy is a universal, temperature-independent functional of density and pair correlation functions for pair potentials.
  • To develop and apply approximate excess entropy functionals for fluids and solids.
  • To enable single-temperature free energy calculations from simulations.

Main Methods:

  • Theoretical analysis of pair potential Hamiltonians.
  • Application of the Kirkwood approximation to fluids and solids.
  • Development of approximate excess entropy functionals.
  • Comparison with thermodynamic integration results.

Main Results:

  • Excess entropy is a universal, temperature-independent functional of density and pair correlation functions.
  • Approximate functionals were developed and validated against thermodynamic integration.
  • The pair functional approach allows absolute entropy and free energy calculation from single-temperature simulation data.

Conclusions:

  • The study extends Henderson's theorem by identifying a temperature-independent excess entropy functional.
  • This approach simplifies free energy calculations, applicable to both fluids and solids.
  • The method holds potential for first-principles calculations using Born-Oppenheimer molecular dynamics.