# How does entropy exactly relate to the heat flow of a system

Entropy is this awesome concept with many faces.

For a classical mechanics point of view, it would represent all the possible properties of a physical system, which is supposed to be unknown.

For a quantum mechanics point of view, it would represent all the possible microstates of a system.

To my knowledge, I assume that the first is a more simple approach of the second, and the second apporach contains the first in it.

So, there would be one basic definition of entropy for both together:

Entropy: The amount of possible microstates a system can have

This is pretty understandable, also I can see that if it is a made-up concept, it can be as abstract as we want, because yeah, words may go beyond reality as much as we want them to.

But, doubts come into the game when we start measuring entropy.

In thermodynamics, we will say that this measure equals the sum of all the infinitely-small-quotients of transferred heat by the temperature of the system, in a reversible process.

$$\Delta S_{12}=\int_1^2 (\frac{\delta Q}{T})_{rev}$$

But how does that relate with the word definition of entropy? How is that quotient of heat divided by temperature related to the microstates?

And, if we cannot speak about stuff having heat, but only about energy flowing in form of heat, and being entropy a heat-related concept, why do we speak about stuff having entropy?

• It is always a good idea to have a look at previous similar questions and related answers. In particular, "How does the statistical definition of entropy reduce to heat engine entropy?" physics.stackexchange.com/questions/301477/… and its answer, should work for your question too. Dec 9 '18 at 17:00
• @GiorgioP Which takes us to this ( physics.meta.stackexchange.com/questions/10898/… ). It "could work" but a) I did not find that question doing a research with my expected keywords and b) Chester's answer goes to the semantic conceptual approach that I was actually looking for, while in your suggested post, it is an advanced mathematical approach that is just partially related to my question. I understand and appreciate your intention but in this case, I think this new Q&A post makes this a richer community now. All the best. Dec 9 '18 at 17:23

Entropy is a physical property of the materials comprising a system in a thermodynamic equilibrium state. And, as you said, it is determined by the number of quantum mechanical micro states that the system can have. In every statistical thermodynamics course, they describe how it is shown that the change in entropy from the quantum mechanical perspective is the same as the change in entropy calculated using the classical heat flow relationship for a reversible process. This is usually done for an ideal gas, and then assumed to extrapolate to other materials. So, there is no direct connection between heat flow and entropy. The heat flow relationship from classical thermodynamics is just a convenient vehicle for quantifying the change in entropy of a system (in lieu of somehow trying to account for all the possible quantum mechanical micro states that the system can have).

• This is a very clear answer to the question. Thank you a lot Chester. Dec 9 '18 at 16:18