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A closed system in thermodynamics is one where no mass is allowed to enter or exit. However, energy can be transferred into or out of the system in the form of heat or work. This is different from an open system, which can exchange both energy and mass with its surroundings. In our problem, the closed system undergoes a process without changing its mass. Only its entropy, a measure of disorder, changes.
When we talk about changes in a closed system, we only consider the changes within the system's boundaries. This simplifies the calculations and focuses on the intrinsic properties, like entropy, temperature, and pressure.

A reversible process is an idealized, hypothetical concept in thermodynamics. It occurs infinitely slowly, so the system remains very close to equilibrium at all times. No real process is truly reversible, but this concept helps us understand the upper limits of efficiency.
In a reversible process, the entropy change \[ \triangle S_{\text{rev}} \] is determined only by the initial and final states. Since our system is closed, the entropy change is expressed as \[ \triangle S_{\text{rev}} = S_2 - S_1 \].
This means that the system's entropy only depends on where it starts and where it ends, not on the path it takes.

An irreversible process, on the other hand, happens spontaneously and often quickly. Real-life processes are typically irreversible. They include factors like friction, unrestrained expansion, rapid mixing, and heat transfer through a finite temperature difference, all of which generate entropy.
Just like the reversible process, the entropy change \[ \triangle S_{\text{irrev}} \] is given by the initial and final states: \[ \triangle S_{\text{irrev}} = S_2 - S_1 \].
However, unlike a reversible process, irreversible processes result in an increase in entropy due to irreversibilities within the system.

Entropy production is a key concept in determining the difference between reversible and irreversible processes. In an internally reversible process, there is no entropy produced; hence \[ \triangle S_{\text{gen}} = 0 \]. This is an ideal scenario where no additional entropy is generated within the system.
For an irreversible process, entropy is always produced. No real process can occur without some entropy production. Hence, \[ \triangle S_{\text{gen, irrev}} > 0 \].
This means that while the total change in entropy between initial and final states remains the same for both reversible and irreversible processes, the entropy produced within the system is greater for the irreversible process.

Thermodynamics is the branch of physics that deals with heat, work, and forms of energy. It helps us understand how energy is transferred and transformed in systems. One of the key principles in thermodynamics involves entropy and the second law, which states that entropy in an isolated system always increases.
By examining reversible and irreversible processes within a closed system, we can better understand how energy efficiency and entropy production are intrinsically linked. The concepts of entropy change and production are vital for deciphering the differences in system behavior between idealized and real-world processes.