# I How to show directly that $\vec{F}=-\mu\vec{v}$ increases entropy?

#### greypilgrim

Hi.

Processes involving a friction force whose direction somehow depends on the direction of the velocity, such as $\vec{F}=-\mu\cdot\vec{v}$, aren't symmetric with respect to time reversal. If you play it backwards, this force would be accelerating.

On the other hand, friction dissipates heat, and that increases entropy. So this is in agreement with thermodynamics.

I wonder: Is it really necessary to assume that friction dissipates heat to see that entropy is increased in such a process? Or is there a more direct or fundamental way to derive that the occurrence of a force like $\vec{F}=-\mu\cdot\vec{v}$ increases entropy, without getting into technicalities?

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#### anorlunda

Mentor
Gold Member
Are you asking about the origin of friction, or about the relationship of friction to energy and entropy?

By the way, a force does not change either entropy or energy. You need force times distance first. And in that light, I don't see any difference between friction force and any other kind of force. Energy is conserved. When you do work, the energy must come from somewhere and go somewhere.

It is true that friction is not time reversible, but neither is it fundamental to physics. Friction is a proxy for the average of many mechanisms that happen on the molecular level, especially the electromagnetic force.

#### Vanadium 50

Staff Emeritus
Science Advisor
Education Advisor
If you play it backwards, this force would be accelerating.
And objects fly up instead of fall down.

#### greypilgrim

And objects fly up instead of fall down.
Which they also do given enough initial upwards velocity, so this is a time reversal symmetric process. In contrast, we never observe an object on a table accelerating due to friction.

By the way, a force does not change either entropy or energy. You need force times distance first.
Sure. I was talking about "processes".

And in that light, I don't see any difference between friction force and any other kind of force. Energy is conserved. When you do work, the energy must come from somewhere and go somewhere.
Yes. And it's all clear if this energy "goes somewhere" as heat, because then it definitely increases entropy. But I wonder if it's necessary to assume that the energy $\vec{F}\cdot d\vec{s}=-\mu\vec{v}\cdot d\vec{s}$ is converted to heat to show that it increases entropy or if this connection is more fundamental, for which the time reversal asymmetry might be an indication.

Maybe I should ask the converse: Can there be a force of the Form $\vec{F}=-\mu\vec{v}$ in a process where the entropy does not increase?

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