# Adiabatic Invariant: Modifying Entropy Derivation by Laura

• lark
In summary, an adiabatic invariant is a physical quantity that remains constant in a system undergoing an adiabatic process, and it is related to entropy through the adiabatic process. Laura's modification to the derivation of entropy using the adiabatic invariant allows for a more accurate calculation of entropy in certain systems. However, this concept can only be applied to systems undergoing adiabatic processes and cannot be applied to non-isolated systems. Examples of systems where the concept of adiabatic invariant is useful include gas expansion and compression, oscillating pendulums, and electromagnetic waves in a vacuum.

#### lark

I modified an incorrect derivation of entropy from phase space volume of a gas in the Wikipedia entry
and I'd like to know if my modified derivation is also incorrect somehow. I realize it doesn't include QM, but I tried to write a sensible classical derivation.
Adiabatic invariants are fascinating to me - I just got exposed to them and interested in the different contexts where they appear. Slowly shortening pendulum, etc.
Laura

It is not clear what was changed.

## 1. What is an adiabatic invariant?

An adiabatic invariant is a physical quantity that remains constant in a system undergoing an adiabatic process, where there is no exchange of heat with the surroundings.

## 2. How does the concept of adiabatic invariant relate to entropy?

The adiabatic invariant is related to entropy through the adiabatic process, where changes in entropy are accompanied by changes in the adiabatic invariant. This means that the adiabatic invariant can be used to modify the derivation of entropy in certain systems.

## 3. What is the significance of Laura's modification to the derivation of entropy using the adiabatic invariant?

Laura's modification allows for a more accurate and precise calculation of entropy in certain systems, by taking into account the conservation of adiabatic invariant. This can lead to a better understanding of thermodynamic processes and their behavior.

## 4. Can the concept of adiabatic invariant be applied to all systems?

No, the concept of adiabatic invariant is only applicable to systems undergoing adiabatic processes, where there is no exchange of heat with the surroundings. It cannot be applied to systems that are not isolated.

## 5. What are some examples of systems where the concept of adiabatic invariant is useful?

Examples of systems where the concept of adiabatic invariant is useful include gas expansion and compression, oscillating pendulums, and electromagnetic waves in a vacuum. In these systems, the adiabatic invariant can help to accurately determine changes in entropy.