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...