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The Second Law of Thermodynamics (2011)

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Re: The Second Law of Thermodynamics (2011)

#11

Post by vinnyvichy »

kgwgk wrote: post #10
vinnyvichy wrote: post #9

Earlier quoted context omitted.

More intuitively: that TdS has the same "units" as -PdV suggests that temperature [difference] is a "pressure" (thermodynamic potential) that drives entropy increase.

It has the same “units” (if you mean “energy”) as mc2 as well and that doesn’t suggest anything to me… Your intuition is much better than mine - or it’s informed by what you know about temperature.

Sorry! I meant they have the same form as used in the energy differential (1-form), but I had thought "units" would make more sense. In fact, this comparison was how I came to the intuition, although, as you coyly suggested, I did do a check with my earlier intuitions..

https://physics.stackexchange.com/questions/415943/why-does-...

Re: The Second Law of Thermodynamics (2011)

#12

Post by kgwgk »

vinnyvichy wrote: post #11
kgwgk wrote: post #10

Earlier quoted context omitted.

It has the same “units” (if you mean “energy”) as mc2 as well and that doesn’t suggest anything to me… Your intuition is much better than mine - or it’s informed by what you know about temperature.

Sorry! I meant they have the same form as used in the energy differential (1-form), but I had thought "units" would make more sense. In fact, this comparison was how I came to the intuition, although, as you coyly suggested, I did do a check with my earlier intuitions.. https://physics.stackexchange.com/questions/415943/why-does-...

I agree that thermodynamic relations - and Legendre transformations - are fascinating. I don’t think I ever fully understood them though - at least not to the point where they became “intuitive” :-)

Re: The Second Law of Thermodynamics (2011)

#13

Post by vinnyvichy »

kgwgk wrote: post #12
vinnyvichy wrote: post #11

Earlier quoted context omitted.

Sorry! I meant they have the same form as used in the energy differential (1-form), but I had thought "units" would make more sense. In fact, this comparison was how I came to the intuition, although, as you coyly suggested, I did do a check with my earlier intuitions.. https://physics.stackexchange.com/questions/415943/why-does-...

I agree that thermodynamic relations - and Legendre transformations - are fascinating. I don’t think I ever fully understood them though - at least not to the point where they became “intuitive” :-)

Erm sorry again to have implied they were intuitive, all I meant was that it was relatively intuitive --maybe i should have said "retrievable in a high-pressure concept-doodling game" --compared to a wall of text..

Re: The Second Law of Thermodynamics (2011)

#14

Post by kgwgk »

vinnyvichy wrote: post #13
kgwgk wrote: post #12

Earlier quoted context omitted.

I agree that thermodynamic relations - and Legendre transformations - are fascinating. I don’t think I ever fully understood them though - at least not to the point where they became “intuitive” :-)

Erm sorry again to have implied they were intuitive, all I meant was that it was relatively intuitive --maybe i should have said "retrievable in a high-pressure concept-doodling game" --compared to a wall of text..

No need to apologize! I was joking, I think I get what you mean.

Re: The Second Law of Thermodynamics (2011)

#15

Post by shiandow »

vinnyvichy wrote: post #9
exmadscientist wrote: post #8

A neat little corollary to this is to look a little more closely at what temperature actually is . "Temperature" doesn't appear too often in the main explanation here, but it's all over the "student's explanation". So... what is it? The most useful definition of temperature at the microscopic scale is probably this one: 1/T = dS / dU, which I've simplified because math notation is hard, and because we're not going to…

More intuitively: that TdS has the same "units" as -PdV suggests that temperature [difference] is a "pressure" (thermodynamic potential) that drives entropy increase.

It's also precisely what will show up if you use Lagrange multipliers to maximize entropy given a fixed energy. (though for that to make sense you're no longer looking at a single state, you're optimizing the probability distribution itself)

Re: The Second Law of Thermodynamics (2011)

#16

Post by vinnyvichy »

kgwgk wrote: post #12
vinnyvichy wrote: post #11

Earlier quoted context omitted.

Sorry! I meant they have the same form as used in the energy differential (1-form), but I had thought "units" would make more sense. In fact, this comparison was how I came to the intuition, although, as you coyly suggested, I did do a check with my earlier intuitions.. https://physics.stackexchange.com/questions/415943/why-does-...

I agree that thermodynamic relations - and Legendre transformations - are fascinating. I don’t think I ever fully understood them though - at least not to the point where they became “intuitive” :-)

If you let me flash you my (still indecent) state of intuition..

"convex conjugates" (more precisely but limited sense "momentum maps") are delimited continuations in a optimization algorithm.

https://en.wikipedia.org/wiki/Convex_conjugate https://en.wikipedia.org/wiki/Delimited_continuation

Re: The Second Law of Thermodynamics (2011)

#17

Post by vinnyvichy »

shiandow wrote: post #15
vinnyvichy wrote: post #9

Earlier quoted context omitted.

More intuitively: that TdS has the same "units" as -PdV suggests that temperature [difference] is a "pressure" (thermodynamic potential) that drives entropy increase.

It's also precisely what will show up if you use Lagrange multipliers to maximize entropy given a fixed energy. (though for that to make sense you're no longer looking at a single state, you're optimizing the probability distribution itself)

Yeah I have been ruminating on the strange coincidence in the naming of Lagrange multipliers, Lagrangian, Lagrangian duals..

(See below about my comment on convex conjugates and delimited continuations)

Re: The Second Law of Thermodynamics (2011)

#18

Post by goatsneez »

2nd law only states a direction, however, does not determine the rate of change of things. It is also related to the spontaneity of reactions. What is the role of activation energy (or other weak/strong nuclear force potential barriers due to state).

What prevents everything happening all at once (just by obeying 2nd law is there a reason?). And if there is, is there a consistent formulation of 2nd law + other law that get this problem, at least macroscopically correct?

Re: The Second Law of Thermodynamics (2011)

#19

Post by 082349872349872 »

vinnyvichy wrote: post #16
kgwgk wrote: post #12

Earlier quoted context omitted.

I agree that thermodynamic relations - and Legendre transformations - are fascinating. I don’t think I ever fully understood them though - at least not to the point where they became “intuitive” :-)

If you let me flash you my (still indecent) state of intuition.. "convex conjugates" (more precisely but limited sense "momentum maps") are delimited continuations in a optimization algorithm. https://en.wikipedia.org/wiki/Convex_conjugate https://en.wikipedia.org/wiki/Delimited_continuation

Delimited continuations are to exponentials as convex conjugates are to implications?

Re: The Second Law of Thermodynamics (2011)

#20

Post by yamrzou »

exmadscientist wrote: post #8

A neat little corollary to this is to look a little more closely at what temperature actually is . "Temperature" doesn't appear too often in the main explanation here, but it's all over the "student's explanation". So... what is it? The most useful definition of temperature at the microscopic scale is probably this one: 1/T = dS / dU, which I've simplified because math notation is hard, and because we're not going to…

I like the following related explanation (https://www.reddit.com/r/thermodynamics/comments/owhkiv/comm...) :

> Many people focus on the statistical definition of entropy and the fact that entropy increases for any spontaneous process. Fewer people are familiar with thinking about entropy as the conjugate thermodynamic variable to temperature. Just as volumes shift to equalize pressure, areas shift to equalize surface tension, and charges shift to equalize voltage, entropy is the "stuff" that shifts to equalize temperature. (Entropy is of course also unique in that it's generated in all four processes.) Entropy is thus in some ways the modern version of the debunked theory of caloric.

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