Discussion of Principal of Order from Disorder

Order and Disorder

Statistical Entropy

 Statistical Entropy is the application of probability theory to the thermodynamic principle of entropy. It has shown that entropy is a measure of the amount of disorder in a system. The mathematical relationship is as follows.

1. The number of equivalent microstates (number of possible ways a given condition to occur is denoted as W.
2. Entropy is denoted as S
3. k is the Boltzmann Constant = 1.38 X 10^-23 JL^-1

S = k ln W

The larger W is the more disordered the system and the larger a system’s entropy.

The smaller W is the more ordered the system is the more disordered it is and the smaller a system’s entropy,

The Second Law of Thermodynamics

The Second Law of Thermodynamics indicates that entropy tends to increase and because entropy is related to disorder, it also indicates that a system’s degree of disorder tends to increase. The only way to decrease a system’s entropy and increase its order is for work to be performed on the system. Now the Second Law of thermodynamics shows that energy applied a system can reduce its entropy but 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. Getting order from disorder requires an additional principle, a principle that relates entropy and energy.

 

Order from Disorder

This additional principle is based on the relationship between the degree of order or disorder with which energy is applied to a system and the degree of order or disorder that it produces in that system.

 

The result is that energy applied to a system in a manner more ordered than that system’s degree of order increases the system’s order and decreases its entropy. On the other hand energy applied to a system in a manner more disordered than that system’s degree of disorder increases the system’s disorder and increases its entropy. The mathematical relationship is as follows.

1. .Number of equivalent microstates of the applied energy is W_e .
2. Number of initial equivalent microstates of the system is W_s .
3. The change in entropy is denoted as DS.
4. 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 the maximum change in the systems entropy but the actual change in entropy results from the amount of energy actually applied to the system .

 

Reduced to it simplest form this principle can be described in two statements:

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

This shows the difference between construction work and a bomb because construction work is less random than that of the raw material and so it decreases its entropy. By contrast a bomb explosion is more random than that of the raw material so it decreases its entropy.

Looking at Statistical Entropy

Statistical Entropy is probability theory applied to entropy showing that it is a measurement a system’s disorder in. Based mainly on the probability of the positions of molecules it explains the tendency; seen in the 2nd Law of Thermodynamics; of entropy to increase. This tendency is because configurations with high entropy are more probable than configurations of low entropy.

The biggest problem with entropy is that it has a tendency to increase. This makes understanding how to decrease entropy is highly important. A common answer is adding energy to the system though that is all that is needed to decrease its entropy.  However this answer is overly simplistic since when energy is applied to a system the way it affects the system’s entropy depends on the way the energy is applied to the system. Consider the difference between construction work and a bomb. Construction work will decrease the entropy of a building under construction. One the other hand a bomb with the same amount of energy and on the same site will inevitably increase the site’s entropy.

This shows that the manner by which energy is applied to a system affects how that energy changes that system’s entropy. What is needed is a general principle that describes this difference and statistical entropy shows exactly how and when entropy can be decreased it shows how to produce order from disorder. Understanding this is critical to a proper study of origins.

Introduction to Statistical Thermodynamics



Statistical Thermodynamics is field of physics that applies probability theory to studying thermodynamics. Statistical Thermodynamics is also known as Statistical Mechanics. Statistical Thermodynamics provides a way to relate the microscopic world of atoms and molecules to the world we see around us, providing a molecular level interpretation of thermodynamic quantities.

Statistically entropy is based on the probability of molecular positions and 2nd Law of Thermodynamics’ tendency of entropy to increase results from high entropy configurations being more probable than low entropy ones.

Statistical Thermodynamics shows us why the laws of Thermodynamics work the way they do and connects the microscopic and macroscopic worlds in a way nothing else can do. It shows why entropy tends to increase and how and when it can be decreased. The fact entropy is related to the number of possible configurations that a system may have is why it can be considered a measurement of the degree of disorder in a system since disrobed systems have more possible configurations than ordered systems.