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Related Concept Videos

Force and Potential Energy in One Dimension01:13

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Newton's first law of motion states that a body at rest remains at rest, or if in motion, remains in motion at constant velocity, unless acted on by a net external force. It also states that there must be a cause for any change in velocity (a change in either magnitude or direction) to occur. This cause is a net external force. For example, consider what happens to an object sliding along a rough horizontal surface. The object quickly grinds to a halt, due to the net force of friction. If...
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Force density functional theory in- and out-of-equilibrium.

Salomée M Tschopp1, Florian Sammüller2, Sophie Hermann2

  • 1Department of Physics, University of Fribourg, CH-1700 Fribourg, Switzerland.

Physical Review. E
|August 17, 2022
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Summary
This summary is machine-generated.

This study introduces a force-based theory for inhomogeneous fluids, using two-body correlations to describe particle interactions. The framework reveals that interparticle forces are density functionals, offering an alternative to standard density functional theory.

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Area of Science:

  • Statistical Mechanics
  • Soft Matter Physics
  • Computational Chemistry

Background:

  • Fluid density becomes inhomogeneous under external fields or confinement.
  • Two-body correlations offer higher resolution than one-body density for fluid microstructure.
  • Interparticle forces are crucial for equilibrium and dynamic properties of fluids.

Purpose of the Study:

  • Develop a theoretical framework for inhomogeneous many-body systems based on two-body correlations.
  • Demonstrate the Yvon-Born-Green (YBG) equation as a local force balance.
  • Show that interparticle forces are functionals of the one-body density.

Main Methods:

  • Utilized local Noether-invariance against spatial distortion.
  • Employed the inhomogeneous Ornstein-Zernike equation.
  • Developed a force-based theory as an alternative to density functional theory.
  • Compared force-based and potential-based density functional theories.

Main Results:

  • Established the Yvon-Born-Green (YBG) equation as a fundamental local force-balance.
  • Demonstrated that two-body correlations are density functionals.
  • Showed force-based theory yields profiles consistent with virial pressure, unlike potential-based theory (compressibility pressure).
  • Proved the hard-wall contact theorem for both approaches.

Conclusions:

  • The force-based theory provides a new perspective on inhomogeneous systems.
  • It offers insights into the nature of correlations in dense and inhomogeneous fluids.
  • The theory reconciles different pressure definitions (compressibility vs. virial) in density functional theory.