My name is Alexander FufaeV and here I write about:

# Entropy Explained on a Microscopic Level

Entropy, abbreviated with the letter $$S$$, is a fundamental concept in thermodynamics. To understand this concept, consider a very simple closed system. A closed system is an isolated part of the universe that does not interact with its surroundings.

The closed system has two subsystems A and B, in which four particles O can reside.

Another concept that is necessary for understanding entropy is the microstate of a system. A microstate of this system is characterized by how the four particles are distributed between the two subsystems. A system usually has many possible microstates. Let's denote their number by $$N$$.

## A system with minimum entropy

Let's construct a system in which no particles can be in subsystem B. All four particles must be in subsystem A:

In order to be able to make a statement about the entropy of this system, the number of possible microstates must be considered. However, the system was constructed in such a way that all particles can ONLY be in A. There is therefore only one microstate of the system, namely the state: »All particles in A«.

This system has a single microstate: $$N = 1$$.

## A system with non-minimal entropy

Let's look at another system where there is more than a single microstate. Let us now assume that there can be a maximum of two particles in subsystem B. The first possible microstate is where all particles are in subsystem A:

The second allowed microstate is where one particle is in subsystem B:

And the last allowed microstate is when there are two particles in subsystem B:

Placing another particle in subsystem B is not permitted in this system. This system has a higher entropy than the previously considered system, where particles could only be in subsystem A.

## A system with maximum entropy

Let us now consider a third system. Let us assume for this system that there are no restrictions on how particles can be distributed in subsystems A and B. Let's go through all possible microstates of the system.

In the first microstate, all particles are in subsystem A:

The second allowed microstate is where there is a single particle in subsystem B:

Der dritte erlaubte Mikrozustand ist, wo zwei Teilchen im Teilsystem B sind:

The next allowed microstate is where there are three particles in subsystem B:

And the last permitted microstate is where all four particles are in subsystem B:

This system has five possible microstates: $$N = 5$$. With only four indistinguishable particles, a maximum of five microstates of this system can be realized.

Which of the three systems has the maximum and minimum entropy? The first system has a single microstate. This system has the lowest entropy $$S_1$$. The second system has three possible microstates. And the third system has five possible microstates. The third system therefore has the highest entropy $$S_3$$.

## Entropy and the second law of thermodynamics

A fundamental law in physics is the second law of thermodynamics. It states the following:

In other words, the number of possible microstates of an isolated system can only increase, not decrease.

The second law of thermodynamics has a serious impact on the future of our universe. Because if the entire universe can be regarded as an isolated system, then entropy will increase over time until it reaches a maximum. At maximum entropy, the number of possible states of the universe will be maximum! And now philosophy comes into play...