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Concept# Entropic force

Summary

In physics, an entropic force acting in a system is an emergent phenomenon resulting from the entire system's statistical tendency to increase its entropy, rather than from a particular underlying force on the atomic scale.
In the canonical ensemble, the entropic force associated to a macrostate partition is given by
where is the temperature, is the entropy associated to the macrostate , and is the present macrostate.
The internal energy of an ideal gas depends only on its temperature, and not on the volume of its containing box, so it is not an energy effect that tends to increase the volume of the box as gas pressure does. This implies that the pressure of an ideal gas has an entropic origin.
What is the origin of such an entropic force? The most general answer is that the effect of thermal fluctuations tends to bring a thermodynamic system toward a macroscopic state that corresponds to a maximum in the number of microscopic states (or micro-states) that are compatible with this macroscopic state. In other words, thermal fluctuations tend to bring a system toward its macroscopic state of maximum entropy.
The entropic approach to Brownian movement was initially proposed by R. M. Neumann. Neumann derived the entropic force for a particle undergoing three-dimensional Brownian motion using the Boltzmann equation, denoting this force as a diffusional driving force or radial force. In the paper, three example systems are shown to exhibit such a force:
electrostatic system of molten salt,
surface tension and,
elasticity of rubber.
Ideal chain
A standard example of an entropic force is the elasticity of a freely jointed polymer molecule. For an ideal chain, maximizing its entropy means reducing the distance between its two free ends. Consequently, a force that tends to collapse the chain is exerted by the ideal chain between its two free ends. This entropic force is proportional to the distance between the two ends. The entropic force by a freely jointed chain has a clear mechanical origin and can be computed using constrained Lagrangian dynamics.

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Entropic force

In physics, an entropic force acting in a system is an emergent phenomenon resulting from the entire system's statistical tendency to increase its entropy, rather than from a particular underlying force on the atomic scale. In the canonical ensemble, the entropic force associated to a macrostate partition is given by where is the temperature, is the entropy associated to the macrostate , and is the present macrostate.

Self-assembly

Self-assembly is a process in which a disordered system of pre-existing components forms an organized structure or pattern as a consequence of specific, local interactions among the components themselves, without external direction. When the constitutive components are molecules, the process is termed molecular self-assembly. Self-assembly can be classified as either static or dynamic. In static self-assembly, the ordered state forms as a system approaches equilibrium, reducing its free energy.

Elasticity (physics)

In physics and materials science, elasticity is the ability of a body to resist a distorting influence and to return to its original size and shape when that influence or force is removed. Solid objects will deform when adequate loads are applied to them; if the material is elastic, the object will return to its initial shape and size after removal. This is in contrast to plasticity, in which the object fails to do so and instead remains in its deformed state. The physical reasons for elastic behavior can be quite different for different materials.

PHYS-441: Statistical physics of biomacromolecules

Introduction to the application of the notions and methods of theoretical physics to problems in biology.

Related lectures (8)

Polymer Conformation: Beyond the Freely Jointed ChainPHYS-441: Statistical physics of biomacromolecules

Explores polymer conformation beyond the Freely Jointed Chain model, emphasizing the importance of correlations and rigidity.

Polymer Theory: End-to-End DistancePHYS-441: Statistical physics of biomacromolecules

Explores the calculation of end-to-end distance in polymer theory, focusing on isotropy, probability distributions, and the Kratky-Porod model.

Polymer Behavior: Force-Extension CurvePHYS-441: Statistical physics of biomacromolecules

Delves into the entropic behavior of polymers through force-extension curves.