Entropic force
Encyclopedia
In physics
, an entropic force acting in a system is a phenomenological
force
resulting from the entire system's statistical tendency to increase its entropy
, rather than from a particular underlying microscopic
force
.
of a freely-jointed polymer
molecule. If the molecule is pulled into an extended configuration, the system has an increased amount of predictability. But randomly coiled configurations are overwhelmingly more probable; i.e., they have greater entropy. This results in the chain eventually returning (through diffusion
) to such a configuration. To the macroscopic observer, the precise origin of the microscopic forces that drive the motion is irrelevant. The observer simply sees the polymer contract into a state of higher entropy, as if driven by an elastic force.
Another example of an entropic force is the hydrophobic
force. It comes from the entropy of the 3D network of water molecules (at room temperature). Each water molecule is capable of
Therefore, water molecules can form an extended three-dimensional network. Introduction of a non-hydrogen-bonding surface disrupts this network. The water molecules rearrange themselves around the surface, so as to minimize the number of disrupted hydrogen bonds. This is in contrast to hydrogen fluoride
(which can accept 3 but donate only 1) or ammonia (which can donate 3 but accept only 1), which mainly form linear chains.
If the introduced surface had an ionic or polar nature, there would be water molecules standing more or less normal to the surface. But a non-hydrogen-bonding surface forces the surrounding hydrogen bonds to be tangential and they are locked in a clathrate-like basket shape. Water molecules involved in this clathrate-like basket around the non-hydrogen-bonding surface are constrained in their orientation. Thus, any event that would minimize such a surface is entropically favored. For example, when two such hydrophobic particles come very close, the clathrate-like baskets surrounding them merge. This releases some of the water molecules into the bulk of the water, leading to an increase in entropy. This is the basis of the so-called "attraction" between hydrophobic objects in water.
(the energy of which depends only on its temperature
, not its volume), the osmotic pressure
of a dilute solution, and in colloidal suspensions, where they are responsible for the crystallization
of hard spheres.
have been argued to be actually entropic in nature. These theories remain speculative and are the subject of ongoing work.
(or arguably a pseudo-force in general relativity
). However, some speculative work, in particular a 2009 theory due to Erik Verlinde
(published in April 2011)., has argued that gravity can be explained as an entropic "force".
For example, when someone throws a ball in the air, it follows a parabolic trajectory
(in the absence of wind resistance). Conventionally, it is said that the ball follows a deterministic path dictated by Newton's law of gravity or general relativity
. However, in the entropic theory, it is argued that the ball can follow any trajectory and picks a trajectory "at random". A calculation demonstrates that, in the collection of possible trajectories, the overwhelming majority are almost exactly the same as the parabolic trajectory. Therefore the ball is observed to follow a parabola.
, the electroweak and strong forces, and dark matter
and dark energy
.
Physics
Physics is a natural science that involves the study of matter and its motion through spacetime, along with related concepts such as energy and force. More broadly, it is the general analysis of nature, conducted in order to understand how the universe behaves.Physics is one of the oldest academic...
, an entropic force acting in a system is a phenomenological
Phenomenology (science)
The term phenomenology in science is used to describe a body of knowledge that relates empirical observations of phenomena to each other, in a way that is consistent with fundamental theory, but is not directly derived from theory. For example, we find the following definition in the Concise...
force
Force
In physics, a force is any influence that causes an object to undergo a change in speed, a change in direction, or a change in shape. In other words, a force is that which can cause an object with mass to change its velocity , i.e., to accelerate, or which can cause a flexible object to deform...
resulting from the entire system's statistical tendency to increase its entropy
Entropy
Entropy is a thermodynamic property that can be used to determine the energy available for useful work in a thermodynamic process, such as in energy conversion devices, engines, or machines. Such devices can only be driven by convertible energy, and have a theoretical maximum efficiency when...
, rather than from a particular underlying microscopic
Microscopic
The microscopic scale is the scale of size or length used to describe objects smaller than those that can easily be seen by the naked eye and which require a lens or microscope to see them clearly.-History:...
force
Force
In physics, a force is any influence that causes an object to undergo a change in speed, a change in direction, or a change in shape. In other words, a force is that which can cause an object with mass to change its velocity , i.e., to accelerate, or which can cause a flexible object to deform...
.
Polymers
A standard example of an entropic force is the elasticityElasticity (physics)
In physics, elasticity is the physical property of a material that returns to its original shape after the stress that made it deform or distort is removed. The relative amount of deformation is called the strain....
of a freely-jointed polymer
Polymer
A polymer is a large molecule composed of repeating structural units. These subunits are typically connected by covalent chemical bonds...
molecule. If the molecule is pulled into an extended configuration, the system has an increased amount of predictability. But randomly coiled configurations are overwhelmingly more probable; i.e., they have greater entropy. This results in the chain eventually returning (through diffusion
Diffusion
Molecular diffusion, often called simply diffusion, is the thermal motion of all particles at temperatures above absolute zero. The rate of this movement is a function of temperature, viscosity of the fluid and the size of the particles...
) to such a configuration. To the macroscopic observer, the precise origin of the microscopic forces that drive the motion is irrelevant. The observer simply sees the polymer contract into a state of higher entropy, as if driven by an elastic force.
Hydrophobic force
Hydrophobe
In chemistry, hydrophobicity is the physical property of a molecule that is repelled from a mass of water....
force. It comes from the entropy of the 3D network of water molecules (at room temperature). Each water molecule is capable of
- donating two hydrogen bondHydrogen bondA hydrogen bond is the attractive interaction of a hydrogen atom with an electronegative atom, such as nitrogen, oxygen or fluorine, that comes from another molecule or chemical group. The hydrogen must be covalently bonded to another electronegative atom to create the bond...
s through the two protons - accepting two more hydrogen bonds through the two sp3 hybridized lone pairs
Therefore, water molecules can form an extended three-dimensional network. Introduction of a non-hydrogen-bonding surface disrupts this network. The water molecules rearrange themselves around the surface, so as to minimize the number of disrupted hydrogen bonds. This is in contrast to hydrogen fluoride
Hydrogen fluoride
Hydrogen fluoride is a chemical compound with the formula HF. This colorless gas is the principal industrial source of fluorine, often in the aqueous form as hydrofluoric acid, and thus is the precursor to many important compounds including pharmaceuticals and polymers . HF is widely used in the...
(which can accept 3 but donate only 1) or ammonia (which can donate 3 but accept only 1), which mainly form linear chains.
If the introduced surface had an ionic or polar nature, there would be water molecules standing more or less normal to the surface. But a non-hydrogen-bonding surface forces the surrounding hydrogen bonds to be tangential and they are locked in a clathrate-like basket shape. Water molecules involved in this clathrate-like basket around the non-hydrogen-bonding surface are constrained in their orientation. Thus, any event that would minimize such a surface is entropically favored. For example, when two such hydrophobic particles come very close, the clathrate-like baskets surrounding them merge. This releases some of the water molecules into the bulk of the water, leading to an increase in entropy. This is the basis of the so-called "attraction" between hydrophobic objects in water.
General chemistry
Entropic forces also occur in the physics of gases and solutions, where they generate the pressure of an ideal gasIdeal gas
An ideal gas is a theoretical gas composed of a set of randomly-moving, non-interacting point particles. The ideal gas concept is useful because it obeys the ideal gas law, a simplified equation of state, and is amenable to analysis under statistical mechanics.At normal conditions such as...
(the energy of which depends only on its temperature
Temperature
Temperature is a physical property of matter that quantitatively expresses the common notions of hot and cold. Objects of low temperature are cold, while various degrees of higher temperatures are referred to as warm or hot...
, not its volume), the osmotic pressure
Osmotic pressure
Osmotic pressure is the pressure which needs to be applied to a solution to prevent the inward flow of water across a semipermeable membrane....
of a dilute solution, and in colloidal suspensions, where they are responsible for the crystallization
Crystallization
Crystallization is the process of formation of solid crystals precipitating from a solution, melt or more rarely deposited directly from a gas. Crystallization is also a chemical solid–liquid separation technique, in which mass transfer of a solute from the liquid solution to a pure solid...
of hard spheres.
Speculative examples
In recent years (especially since 2009) some forces that are generally regarded as conventional forcesForce
In physics, a force is any influence that causes an object to undergo a change in speed, a change in direction, or a change in shape. In other words, a force is that which can cause an object with mass to change its velocity , i.e., to accelerate, or which can cause a flexible object to deform...
have been argued to be actually entropic in nature. These theories remain speculative and are the subject of ongoing work.
Gravity
It is generally believed that gravity is a microscopic forceForce
In physics, a force is any influence that causes an object to undergo a change in speed, a change in direction, or a change in shape. In other words, a force is that which can cause an object with mass to change its velocity , i.e., to accelerate, or which can cause a flexible object to deform...
(or arguably a pseudo-force in general relativity
General relativity
General relativity or the general theory of relativity is the geometric theory of gravitation published by Albert Einstein in 1916. It is the current description of gravitation in modern physics...
). However, some speculative work, in particular a 2009 theory due to Erik Verlinde
Erik Verlinde
Erik Peter Verlinde is a Dutch theoretical physicist and string theorist. He is the identical twin brother of physicist Herman Verlinde. The Verlinde formula, which is important in conformal field theory and topological field theory, is named after him. His research deals with string theory,...
(published in April 2011)., has argued that gravity can be explained as an entropic "force".
For example, when someone throws a ball in the air, it follows a parabolic trajectory
Parabolic trajectory
In astrodynamics or celestial mechanics a parabolic trajectory is a Kepler orbit with the eccentricity equal to 1. When moving away from the source it is called an escape orbit, otherwise a capture orbit...
(in the absence of wind resistance). Conventionally, it is said that the ball follows a deterministic path dictated by Newton's law of gravity or general relativity
General relativity
General relativity or the general theory of relativity is the geometric theory of gravitation published by Albert Einstein in 1916. It is the current description of gravitation in modern physics...
. However, in the entropic theory, it is argued that the ball can follow any trajectory and picks a trajectory "at random". A calculation demonstrates that, in the collection of possible trajectories, the overwhelming majority are almost exactly the same as the parabolic trajectory. Therefore the ball is observed to follow a parabola.
Other forces
Other forces have been argued recently to be entropic in origin, including Coulomb's lawCoulomb's law
Coulomb's law or Coulomb's inverse-square law, is a law of physics describing the electrostatic interaction between electrically charged particles. It was first published in 1785 by French physicist Charles Augustin de Coulomb and was essential to the development of the theory of electromagnetism...
, the electroweak and strong forces, and dark matter
Dark matter
In astronomy and cosmology, dark matter is matter that neither emits nor scatters light or other electromagnetic radiation, and so cannot be directly detected via optical or radio astronomy...
and dark energy
Dark energy
In physical cosmology, astronomy and celestial mechanics, dark energy is a hypothetical form of energy that permeates all of space and tends to accelerate the expansion of the universe. Dark energy is the most accepted theory to explain recent observations that the universe appears to be expanding...
.
See also
- ColloidColloidA colloid is a substance microscopically dispersed evenly throughout another substance.A colloidal system consists of two separate phases: a dispersed phase and a continuous phase . A colloidal system may be solid, liquid, or gaseous.Many familiar substances are colloids, as shown in the chart below...
s - NanomechanicsNanomechanicsNanomechanics is a branch of nanoscience studying fundamental mechanical properties of physical systems at the nanometer scale. Nanomechanics has emerged on the crossroads of classical mechanics, solid-state physics, statistical mechanics, materials science, and quantum chemistry...
- Data clusteringData clusteringCluster analysis or clustering is the task of assigning a set of objects into groups so that the objects in the same cluster are more similar to each other than to those in other clusters....
- Entropic elasticity of an ideal chain