translate.google translates the French text of fxp’s website post
Entropy characterizes the increase in the complexity of a system, ie the amount of information that is necessary to describe (solve) it.
At the outset, we consider a closed system, that is to say a system which exchanges neither energy (mechanical, thermal, radiation) nor matter with its environment.
Entropy is linked to the notion of disorder: the more information there is necessary to describe a system, the more it can appear to us to be disordered.
In fact, entropy is a concept of physics linked to the precise measurement of notions of order or disorder. Entropy also measures the capacity to evolve for a closed system having a certain usable energy (because having a low entropy).
If you have a team in which the horses are going in all directions you cannot move forward because there is no order.
If you discipline your horses then their ordered energy becomes usable to move the team forward.
This example shows that energy (the force that horses can mobilize to do a certain job) is not sufficient and that there is also a notion of order which is very important. It is the concept of entropy that is linked to this order or this disorder.
Energy is what allows evolution, change. If a car’s gas tank is empty, it cannot move forward unless it uses the potential gravitational energy it has or the kinetic energy it has accumulated on a slope, which will allow you if you are lucky, to get to the next gas pump.
If the entropy is low (ordered system) the system can evolve.
As it evolves, entropy increases, ie energy degrades (decreases its order) and the system is less able to evolve.
For example, horses will consume the chemical energy contained in the food they have eaten by using oxygen from the air through respiration to produce ATP molecules Adenosine_triphosphate_ which is the fuel of physiology. By pulling the hitch they will consume this fuel to operate the muscles (the engine).
When the energy of all the food has been consumed with possibly the reserves stored in their muscles, their liver and their fat then they will be tired, will have to rest and if they do not eat again (closed system) they will not be able to well. continue to pull the team for a long time if not until exhaustion (energy reserves).
Consuming energy is in fact increasing entropy because we never consume energy because of the law of conservation of energy which is the first principle of thermodynamics: in a closed system, energy is constant .
When energy is dissipated or degraded, its entropy therefore increases its disorder (this is the second principle of thermodynamics).
In the example of horses, the horse dung resulting from digestion is less orderly than the herbs from which it is derived.
It is the low entropic energy of the sun that photosynthesizes the grasses to regrow using organic matter in the horse manure.
Entropy is a notion initially introduced in macroscopic thermodynamics by Clausius.
Rudolf_Clausius_ and whose deep meaning in terms of information was clarified much later in statistical mechanics by Boltzmann_.
The second principle of thermodynamics says that in a closed system, entropy can only increase or at the limit, remain constant.
Order and disorder are of fundamental importance in physics which deals with the operating laws of physical systems composed of a very large number of entities (a gas formed by all of its molecules for example) . This physics is called Thermodynamics_.
Large numbers reveal new properties, new concepts, new realities and experiences.
Entropy was then redefined by Shannon_ as part of information theory where entropy is identified with the amount of information.
(Information theory is the basis of computer science, so entropy must play an important role in this area of entropy and computing.)
Entropy and information
Entropy and information are strongly related concepts and can be considered the same in statistical mechanics.
In fact, the more complex a system, the greater its entropy and the more information is needed to describe it.
For example, the same quantity of matter in the form of gas or in the form of a crystal is not described with the same quantity of information. If the crystal is perfect (without gap, or dislocation, etc.) then it suffices to specify the position of an atom of the crystal and the structure of the crystal lattice to know where all the atoms of the crystal are located. So very little information is needed to describe the system.