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Order from Disorder
and reducing entropy


Statistical Entropy

Classically entropy is the measure of a system's thermal energy unavailable for conversion into mechanical work.

Statistical Entropy is the application of probability theory to the thermodynamic principle of entropy. It shows that entropy is a measure of the amount of disorder in a system

The number of equivalent microstates denoted as W is the number of possible ways for a given condition of a system can occur.

Entropy is denoted as S

k is the Boltzmann Constant = 1.38 X 10-23 JL-1

S = k ln W

This shows that entropy is a measure of the disorder of a system because disordered systems have more equivalent microstates than ordered systems. As a result the larger W is the more disordered the system and the smaller W is the more ordered the system is. This means that the larger a system’s entropy the more disordered it is the smaller a system’s entropy the more ordered it is. So produce order from disorder you need to reduce a system's entropy


The Second Law of Thermodynamics

The Second Law of Thermodynamics indicates that entropy tends to increase and this is because entropy is related to disorder. As a result it also indicates that a system’s degree of disorder tends to increase. The only way to decrease a system’s entropy and there by increase its order is for work to be performed on the system.

However while the Second Law shows that energy applied a system can reduce its entropy, it does not show how the manner in which energy is applied affects entropy.  That is it does not show the deference between construction work and a bomb. Construction work reduces a system’s entropy while bombs increase a system’s entropy. Unfortunately the Second Law  does not show the difference so as a result an additional principle is needed to show this difference.


Order from Disorder

This additional principle relates the degree of order or disorder with which energy is applied to a system to the degree of order or disorder that it produces in that system. Such that if energy is applied to a system in a manner more ordered than that system’s degree of order then it increases the system’s order. On the other hand if energy is applied to a system in a manner more disordered than that system’s degree of disorder then it increases the system’s disorder.

To show the mathematical relationship with entropy let’s define the following.

Number of equivalent microstates of the applied energy is We

Number of initial equivalent microstates of the system is W

 The change in entropy is denoted as DS

k is the Boltzmann Constant = 1.38 X 10-23 JL-1 

This shows the general direction that applying energy to a system will move the entropy of that system as well as maximum change in entropy that will occure. The actual change in entropy results from the amount of energy actually applied to the system.  This principle can be reduced to two statements

The general application of energy to a system in a manner more random than that system will increase the entropy of that system.

The general application of energy to a system in a manner less random than that system will decrease the entropy of that system.


Examples of this Principle

The following are examples of this principle in action.

This principle shows the difference between construction work and a bomb. Construction work is less random than the degree of randomness of the raw material so it decreases its entropy. A bomb explosion on the other hand is more random than the degree of  randomness of the raw material so it decreases its entropy.

Consider what happens when a system is heated or cooled.  Because at the molecular level, heat energy is applied in a manner more random than the system, heat increases entropy.  However as a system cools the electromagnetic forces between molecules applies energy in a manner less random than the system, so cooling decreases entropy.

The goal of straitening up a room is to reduce the room’s entropy that is making order from disorder. So if you just toss things around the rooms in a manner more random than they already are you will actually increase the room’s entropy. If instead you place things around a room in a more ordered manner than they already are you will decrease the room’s entropy.


What this Principle Shows Us

This principle applies to all systems since it is both system and path independent. That is that the concept does not rely on any details about the system or the exact way the energy takes the system from one state to the other. The basic principle is that adding more randomness to a system makes it more random and adding more order to a system makes it more organized. It shows that it get a given degree of order form disorder one needs to apply energy to a system with at least the same degree of order. This means that to get a given degree of order in a system you need at least that same degree of order outside the system.


Application to Life

Living systems are generally conservation systems in that the increase of their entropy over time is generally slower than that of non-living systems. The reason living systems are generally conservative is that they apply energy to maintain themselves against degeneration. However they still increase their entropy because no mater how organized this application of energy is it is still always a little more disordered than the living system. As a result living systems increase their entropy over time but just more slowly than a non living system.

This principle has a lot to say about the origin of life and how it got started however this is a topic for another article.


Conclusion

Applying energy to a system in a manner more random than the system increases that systems randomness.  However applying energy to a system in a manner more ordered than the system increases that systems order. It turns out that to raise a system to a given degree of order requires applying energy in a manner with at least the same degree of order. This means that to get order you need order.


Reference

Entropy and Applied Energy
A reprint of the original paper on the affect on entropy of the application of energy to a system.
 

 


 

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