The One About The Force Of Entropy

ENTROPIC FORCEx

I'm trying to understand cosmology, why the Big Bang had the properties it did. And it's interesting to think that connects directly to our kitchens and how we can make eggs, how we can remember one direction of time, why causes precede effects, why we are born young and grow older. It's all because of entropy increasing.

-Sean M. Carroll

Any thermodynamic system in nature tries to maximize its entropy during the course of a spontaneous ie. self-driven process.

Entropic force is merely the physical manifestation of the second law of thermodynamics as stated above. It is the phenomenon resulting from the tendency of a system to increase its entropy or equivalently, ensure the maximum dispersal of its energy. Note that here entropy is defined as a measure of energy dispersal unlike the conventional sense of it being a measure of disorder. The modification made to its definition is to allow for a more objective definition of the term as the incumbent (measure of disorder) is unable to quantify entropy in its pure mathematical form.

However entropic force, though not regarded as one of the four fundamental forces by mere convention, plays an important role in completing our picture of the Universe as there are several phenomena which cannot be explained using the four fundamental forces such as the simple phenomenon of osmosis or even the spontaneous creation of life on Earth.

The  still role played by entropic force in establishing sentient life on the planet is depicted in the, part-fiction, book 'Origin' by Dan Brown.


Entropic force can be mathematically formulated as such-

where X(0) is the initial micro-state of the system under observation and where the force originates and X is the final micro-state ie. the state to which the entropic force is driving the system towards.

The existence of an entropic force is vital to the explanation of the following processes, among several others :

1.Mach's Principle
2.Heat Dispersion
3.Pressure of an ideal gas
4.Brownian Motion


1. Mach's Principle

Mach's principle is extremely abstract and states that local physical laws are determined by the large scale interaction of the universe. It also generically states that the inertia of a body is determined by the inertia of all the other bodies in the universe.
Such a relationship can only be proven by the existence of a long range force that can transmit the effects of a change in one part of the universe or the system under consideration to the rest of it without the transfer of particulate matter or field particles (gauge bosons). This force is entropic force.

2.Heat Dispersion

The process of  heat conduction by means of short range action can be explained by means of an entropic force. When one part of a rod or any solid substance is heated, a non-uniform distribution of heat energy is created as a result of which the entropy of the system becomes lesser than the maximum value it can attain with that energy- which is with maximum energy distribution.Thus the particles of the system will interact with one another to create a homogeneous distribution of energy and thus maximize energy

3.Pressure Of An Ideal Gas

An ideal gas is one whose internal energy depends upon its temperature. However the pressure of an ideal gas tends to increase its volume. Thus the pressure of the gas has an entropic origin.

Also due to the absence of interaction between the particles, the pressure of an ideal gas is due to the thermal excitation and motion of the particles of the gas. The thermal motion of the gas is itself due to the tendency of the system to attempt to bring its particles in a state where they occupy the microstates that correspond to the macro-state of highest entropy.

4. Brownian Motion

Brownian motion is the random movement of particles in a fluid due to uneven bombardment by the particles of the fluid.

A theory was propounded that states that Brownian motion is driven by an entropic force.

Thus entropic forces govern a variety of natural phenomena and are staking a serious claim to emerge as the fifth fundamental force.As recently as 2009, Dutch researcher Erik Verlinde also proposed that gravity and all the forces as described by Newton's second law could be of entropic origin.
Thus the field of entropic forces (Ironic as entropic force is not associated with a field 😂)is a rapidly emerging field full of interesting developments and one to watch for in the future.


Additional Reading Material

1. Miller Urey Experiment
2. Gravity as an Entropic Force by Verlinde
3. Entropic Forces In Brownian Motion
4.Mathematical Formulation of Entropic Force
5.A Counterpoint - Why Gravity is not an Entropic Force
6.Statistics of Entropic Forces
7.Hydrophobic Entropic Force