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The Second Law of Thermodynamics (2011)

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Re: The Second Law of Thermodynamics (2011)

#21

Post by n_plus_1_acc »

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 this explanation, but I feel it builds on a good understanding of entropy

Re: The Second Law of Thermodynamics (2011)

#22

Post by vinnyvichy »

082349872349872 wrote: post #19
vinnyvichy wrote: post #16

Earlier quoted context omitted.

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?

I'm pretty sure I don't understand the possible meanings of what you said there either so let's try :)

I meant that the tangent to the convex conjugate ("momentum") provides bounds on what the values returned by the dual step in a primal-dual algo should be. I don't know which meaning of "exponential" I should focus on here (the action perhaps? A power set? A probability distribution?), but "implications" seem to refer to a constraint on outputs contingent on the inputs so I will go with that. Delimited continuations seem to be the closest thing I found in the PL lit, aka wikipedia, feel free to suggest something less kooky :)

Re: The Second Law of Thermodynamics (2011)

#23

Post by yamrzou »

n_plus_1_acc wrote: post #21
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 this explanation, but I feel it builds on a good understanding of entropy

If you want an independent definition of temperature without reference to entropy, you might be interested in the Zeroth Law of Thermodynamics (https://en.wikipedia.org/wiki/Zeroth_law_of_thermodynamics).

Here is a intuitive explanation for it from [1]:

“Temperature stems from the observation that if you bring physical objects (and liquids, gases, etc.) in contact with each other, heat (i.e., molecular kinetic energy) can flow between them. You can order all objects such that:

- If Object A is ordered higher than Object B, heat will flow from A to B.

- If Object A is ordered the same as Object B, they are in thermal equilibrium: No heat flows between them.

Now, the position in such an order can be naturally quantified with a number, i.e., you can assign numbers to objects such that:

- If Object A is ordered higher than Object B, i.e., heat will flow from A to B, then the number assigned to A is higher than the number assigned to B.

- If Object A is ordered the same as Object B, i.e., they are in thermal equilibrium, then they will have the same number.

This number is temperature.”

[1] https://physics.stackexchange.com/a/727798/36360

Re: The Second Law of Thermodynamics (2011)

#24

Post by [deleted] »

j16sdiz wrote: post #7
Harmohit wrote: post #5

As another comment mentioned, this website does look like Time Cube at first sight. However, the explanations of the second law of thermodynamics on the second page are quite decent and written in a humorous way. Of course it is not fully accurate because it does not use any math but I think it does a good enough job of explaining it to the lay person. The explanations about human life at the third page are analogous…

[flagged]

[deleted]

Re: The Second Law of Thermodynamics (2011)

#25

Post by bollu »

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…

Does the temperature actually change discontinuously in a physical system from -infty to +infty, or is it a theoretical artifact that does not show up experimentally?

Re: The Second Law of Thermodynamics (2011)

#26

Post by kgwgk »

bollu wrote: post #25
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…

Does the temperature actually change discontinuously in a physical system from -infty to +infty, or is it a theoretical artifact that does not show up experimentally?

Depending on what you mean by “discontinuously” it always does: the microscopic world is “discrete”.

Instead of thinking of “temperature” you may think of “inverse of temperature” and then there is no issue with that number going “continously” from very negative to very positive.

Re: The Second Law of Thermodynamics (2011)

#28

Post by meindnoch »

yamrzou wrote: post #23
n_plus_1_acc wrote: post #21

Earlier quoted context omitted.

I like this explanation, but I feel it builds on a good understanding of entropy

If you want an independent definition of temperature without reference to entropy, you might be interested in the Zeroth Law of Thermodynamics ( https://en.wikipedia.org/wiki/Zeroth_law_of_thermodynamics ). Here is a intuitive explanation for it from [1]: “Temperature stems from the observation that if you bring physical objects (and liquids, gases, etc.) in contact with each other, heat (i.e., molecular kinetic ener…

Yes, but this still allows infinitely many "temperature" scales. I.e. take the current definition of temperature, and apply any nondecreasing function to it.

Re: The Second Law of Thermodynamics (2011)

#29

Post by robaato »

The classic Flanders and Swann explanation: https://www.youtube.com/watch?v=VnbiVw_1FNs

Excerpts: No one can consider themsleves educated who doesn't understand the basic language of science - Boyle's law: the greater the external pressure the greater the volume of hot air. I was someone shocked to learn my partner not only doesn't understand the 2nd law of thermodynamics, he doesn't even understand the first!

: Heat won't pass from the cooler to hotter! You can try it if you like but you'd far better notta!

M: Heat is work and work's a curse M: And all the heat in the universe M: Is gonna cool down, M: 'Cos it can't increase M: Then there'll be no more work M: And there'll be perfect peace D: Really? M: Yeah, that's entropy, Man.

Re: The Second Law of Thermodynamics (2011)

#30

Post by jwmerrill »

yamrzou wrote: post #23
n_plus_1_acc wrote: post #21

Earlier quoted context omitted.

I like this explanation, but I feel it builds on a good understanding of entropy

If you want an independent definition of temperature without reference to entropy, you might be interested in the Zeroth Law of Thermodynamics ( https://en.wikipedia.org/wiki/Zeroth_law_of_thermodynamics ). Here is a intuitive explanation for it from [1]: “Temperature stems from the observation that if you bring physical objects (and liquids, gases, etc.) in contact with each other, heat (i.e., molecular kinetic ener…

From later in [1]

> Mind that all of this does not impose how we actually scale temperature.

> How we scale temperature comes from practical applications such as thermal expansion being linear with temperature on small scales.

An absolute scale for temperature is determined (up to proportionality) by the maximal efficiency of a heat engine operating between two reservoirs: e = 1 - T2/T1.

This might seem like a practical application, but intellectually, it’s an important abstraction away from the properties of any particular system to a constraint on all possible physical systems. This was an important step on the historical path to a modern conception of entropy and the second law of thermodynamics [2].

[1] https://physics.stackexchange.com/a/727798/36360

[2] https://bayes.wustl.edu/etj/articles/ccarnot.pdf

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