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Related Concept Videos

Entropy02:39

Entropy

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...
Entropy01:18

Entropy

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...
Entropy Changes Accompanying Specific Processes01:21

Entropy Changes Accompanying Specific Processes

Entropy, a measure of disorder in a system, changes during phase transitions like freezing or boiling. At the transition temperature Ttrs, where two phases are in equilibrium, the phase transition is a reversible process. The entropy change can be calculated from a substance's enthalpy of transition using the equation ΔStrs = ΔtrsH /Ttrs.When a perfect gas expands isothermally from one volume to another, entropy increases logarithmically with volume. Conversely, isothermal compression results...
Entropy and the Second Law of Thermodynamics01:20

Entropy and the Second Law of Thermodynamics

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...
Entropy and the Second Law of Thermodynamics01:26

Entropy and the Second Law of Thermodynamics

Consider an isolated system in which a hot object is placed in contact with a cold one. This is an irreversible process that eventually leads both objects to reach the same equilibrium temperature. It is crucial to note that the constituents of any substance exhibit increased disorder at higher temperatures. As a cold substance absorbs heat, its constituents become more disordered. The energy transfer from a hotter object to a cooler one increases the system's disorder or randomness. This...
Entropy and Solvation02:05

Entropy and Solvation

The process of surrounding a solute with solvent is called solvation. It involves evenly distributing the solute within the solvent. The rule of thumb for determining a solvent for a given compound is that like dissolves like. A good solvent has molecular characteristics similar to those of the compound to be dissolved. For example, polar solutions dissolve polar solutes, and apolar solvents dissolve apolar solutes. A polar solvent is a solvent that has a high dielectric constant (ϵ ≥ 15); an...

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Visualization of Failure and the Associated Grain-Scale Mechanical Behavior of Granular Soils under Shear using Synchrotron X-Ray Micro-Tomography
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Visualization of Failure and the Associated Grain-Scale Mechanical Behavior of Granular Soils under Shear using Synchrotron X-Ray Micro-Tomography

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Coarse-graining entropy, forces, and structures.

Joseph F Rudzinski1, W G Noid

  • 1Department of Chemistry, The Pennsylvania State University, University Park, Pennsylvania 16802, USA.

The Journal of Chemical Physics
|December 14, 2011
PubMed
Summary
This summary is machine-generated.

This study reveals that structure- and force-based coarse-grained (CG) modeling methods share fundamental connections. Both approaches can be unified through an information function, with differences emerging in specific coordinate systems and basis sets.

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Area of Science:

  • Computational Chemistry and Physics
  • Materials Science
  • Statistical Mechanics

Background:

  • Coarse-grained (CG) models are essential for simulating complex systems beyond the reach of atomistic detail.
  • Parameterization of CG models typically follows either force- or structure-motivated strategies.
  • The relationship between these distinct parameterization approaches remains an active area of research.

Purpose of the Study:

  • To investigate the theoretical parallels between force- and structure-motivated coarse-grained modeling.
  • To unify the relative entropy and multiscale coarse-graining (MS-CG) methods under a common information-theoretic framework.
  • To analyze the conditions for potential uniqueness and extend existing formalisms.

Main Methods:

  • Formulation of both relative entropy and MS-CG methods in terms of a shared information function.
  • Analysis of the minimization principles associated with each approach (average information vs. average squared gradient).
  • Generalization of potential uniqueness conditions and extension of MS-CG and Yvon-Born-Green formalisms.
  • Numerical calculations using varying basis sets (complete, incomplete harmonic, higher-order polynomials, curvilinear coordinates).

Main Results:

  • Demonstrated that both relative entropy and MS-CG methods can be expressed using an information function.
  • Identified that relative entropy minimizes the average information function, while MS-CG minimizes the average squared gradient.
  • Established conditions for the uniqueness of structure-based potentials, mirroring MS-CG conditions.
  • Numerical results show identical outcomes for complete and incomplete harmonic Cartesian basis sets.
  • Observed discrepancies when using higher-order polynomial or curvilinear coordinate basis sets.

Conclusions:

  • Force- and structure-based CG model parameterization methods are fundamentally linked.
  • The choice of basis set and coordinate system significantly impacts the agreement between the two approaches.
  • This work provides a unified perspective on CG model parameterization, advancing simulation efficiency and accuracy.