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Demystifying the second law of thermodynamics

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Re: Demystifying the second law of thermodynamics

#21

Post by adeledeweylopez »

zug_zug wrote: post #16

There's something about attempts at entropy that feels entirely inadequate. The definition of "law" in science isn't something that's true, just something that we haven't observed any exceptions to (yet). However entropy, is in larger systems entirely unmeasurable as far as I understand (is there even a unit for it?). Rather than tackle-these scientific shortcomings head-on, most tend to gloss over it. Perhaps a good…

Entropy is a measure of the uncertainty that an observer has over the microstates (i.e. the exact state of every atom) given their knowledge of the macrostate (i.e. what they are capable of describing: like "the water is just above freezing"). So it's inherently a subjective concept. The most common unit for entropy is the bit, same unit as information.

Anyway, entropy is measurable just like any other physical quantity. You need to determine what your model of the microstates is (often an "ideal gas", with independent molecular point particles with their own positions and velocities, and all interactions are perfectly elastic collisions), what you currently know (stuff like type of gas, pressure/volume/temperature), and then there is a clear answer to what the entropy is.

The true law underlying the second law of thermodynamics is conservation of information. In (classical) physics, this is typically cast as Liouville's theorem, which shows that the area of the phase space of a system must remain constant. (In quantum, it's only true for unitary transformations, which may or may not be everything depending on your interpretation of QM).

Anyway, if you're curious about learning more, I highly recommend http://www.av8n.com/physics/thermo which is an amazing online (and free) book that clarifies the concepts of thermodynamics brilliantly.

Re: Demystifying the second law of thermodynamics

#22

Post by adeledeweylopez »

taliesinb wrote: post #2

It’s probably been 15 years since I looked in detail at a formal treatment of statistical mechanics, so maybe this is well-trodden territory, but... has anyone formalized the idea that the second law can be interpreted as a general inability of computer programs to predict one another? I’m also channeling Wolfram here, but I’m not sure if he ever expressed it exactly this way. But the thing I’m imagining would be: se…

Yeah! You can derive the second law from "conservation of information".

This is a great resource about thermodynamics which goes into some of these ideas: http://www.av8n.com/physics/thermo

Re: Demystifying the second law of thermodynamics

#23

Post by Geminidog »

abdullahkhalids wrote: post #12
zug_zug wrote: post #3

This is speaking of entropy and states of gasses. Isn't there some generalization of entropy, such that even when sentient life-forms tried their damnedest, or even in black-holes, entropy must always trend up? Or was that a mischaracterization?

The laws of physics, as far as we understand and have checked, are exactly the same for sentient life, as they are for "dead" matter. In any closed system (which might include sentient life) it is impossible for entropy to decrease, no matter how much the sentient life tries to stop this from happening.

The article above just proved it's possible using math. From an intuitive standpoint it's also easy to see why entropy can decrease. However the problem is, most people don't have a good intuition of what entropy is....

Entropy is a probabilistic phenomena. Meaning that entropy can go lower, it's just that there is a low probability of it happening.

So for example random particles in a closed system do have the potential of self organizing into a cube but it's just a very very low probability.

Even the sentence above distracts from what entropy truly is because our solar system is an example of particles self organizing into spheres rather than cubes.

Here's another example: Flat cylindrical Magnets will self organize into stacks. When the magnets are scattered entropy is lower, when the magnets self organize into a stack entropy has reached it's highest equilibrium point.

Once you understand why the above occurs in the context of entropy than you truly understand the concept. Until then most people don't understand it at all and explain away the self organization with some temperature increase happening somewhere else in the system.

The logic above holds the flaw that the system is still self organizing by shifting temperature to other regions in the system. Moving temperature or disorder to specific regions in a system is still self organization.

Re: Demystifying the second law of thermodynamics

#24

Post by flubert »

taliesinb wrote: post #20
flubert wrote: post #17

Earlier quoted context omitted.

>has anyone formalized the idea that the second law can be interpreted as a general inability of computer programs to predict one another? Arieh Ben Naim thinks entropy is better described by Shannon's Measure of Information. I haven't actually read any of his books, but I've been meaning to "one of these days". http://ariehbennaim.com/books/index.html

Frustrating, that list contains almost no usable links. Its as if he doesn’t want you to actually read or understand what he is saying.

  - Entropy Demystified: The Second Law Reduced To Plain Common Sense
(https://www.amazon.com/Entropy-Demystified-Second-Reduced-Co...)

  - A Farewell to Entropy
(https://www.amazon.com/Farewell-Entropy-Statistical-Thermody...)

  - Discover Entropy and the Second Law
(https://www.amazon.com/Discover-Entropy-Second-Law-Thermodyn...)

  - Entropy And The Second Law: Interpretation And Misss-Interpretationsss
(https://www.amazon.com/Entropy-Second-Law-Interpretation-Mis...)

  - Information, Entropy, Life and the Universe
(https://www.amazon.com/Information-Entropy-Life-Universe-Wha...)

  - Entropy: The Truth, The Whole Truth, And Nothing But The Truth
(https://www.amazon.com/Entropy-Truth-Whole-Nothing-But/dp/98...)

  - Four Laws That Do Not Drive The Universe, The: Elements Of Thermodynamics For The Curious And Intelligent
(https://www.amazon.com/Four-Laws-That-Drive-Universe/dp/9813...)

  - TIME'S ARROW (?): The Timeless Nature of Entropy and the Second Law of Thermodynamics
(https://www.amazon.com/TIMES-ARROW-Timeless-Entropy-Thermody...)

  - Entropy for Smart Kids and their Curious Parents
(https://www.amazon.com/Entropy-Smart-their-Curious-Parents/d...)

Re: Demystifying the second law of thermodynamics

#25

Post by joycian »

adeledeweylopez wrote: post #21
zug_zug wrote: post #16

There's something about attempts at entropy that feels entirely inadequate. The definition of "law" in science isn't something that's true, just something that we haven't observed any exceptions to (yet). However entropy, is in larger systems entirely unmeasurable as far as I understand (is there even a unit for it?). Rather than tackle-these scientific shortcomings head-on, most tend to gloss over it. Perhaps a good…

Entropy is a measure of the uncertainty that an observer has over the microstates (i.e. the exact state of every atom) given their knowledge of the macrostate (i.e. what they are capable of describing: like "the water is just above freezing"). So it's inherently a subjective concept. The most common unit for entropy is the bit, same unit as information. Anyway, entropy is measurable just like any other physical quant…

Could you recommend more like that?

Re: Demystifying the second law of thermodynamics

#26

Post by taliesinb »

adeledeweylopez wrote: post #22
taliesinb wrote: post #2

It’s probably been 15 years since I looked in detail at a formal treatment of statistical mechanics, so maybe this is well-trodden territory, but... has anyone formalized the idea that the second law can be interpreted as a general inability of computer programs to predict one another? I’m also channeling Wolfram here, but I’m not sure if he ever expressed it exactly this way. But the thing I’m imagining would be: se…

Yeah! You can derive the second law from "conservation of information". This is a great resource about thermodynamics which goes into some of these ideas: http://www.av8n.com/physics/thermo

Hey Adele! Thanks for the resource. Here's something a bit wilder I'm still trying to wrap my head around:

https://www.sciencedirect.com/science/article/abs/pii/S09252...

Re: Demystifying the second law of thermodynamics

#27

Post by taliesinb »

flubert wrote: post #24
taliesinb wrote: post #20

Earlier quoted context omitted.

Frustrating, that list contains almost no usable links. Its as if he doesn’t want you to actually read or understand what he is saying.

- Entropy Demystified: The Second Law Reduced To Plain Common Sense ( https://www.amazon.com/Entropy-Demystified-Second-Reduced-Co... ) - A Farewell to Entropy ( https://www.amazon.com/Farewell-Entropy-Statistical-Thermody... ) - Discover Entropy and the Second Law ( https://www.amazon.com/Discover-Entropy-Second-Law-Thermodyn... ) - Entropy And The Second Law: Interpretation And Misss-Interpretationsss ( https://www…

Thanks, I do appreciate you extracting this. I did follow one or two of these originally. But I'm not going to buy an ebook on Amazon to figure out if he has anything useful to say.

Re: Demystifying the second law of thermodynamics

#28

Post by flubert »

taliesinb wrote: post #27
flubert wrote: post #24

Earlier quoted context omitted.

- Entropy Demystified: The Second Law Reduced To Plain Common Sense ( https://www.amazon.com/Entropy-Demystified-Second-Reduced-Co... ) - A Farewell to Entropy ( https://www.amazon.com/Farewell-Entropy-Statistical-Thermody... ) - Discover Entropy and the Second Law ( https://www.amazon.com/Discover-Entropy-Second-Law-Thermodyn... ) - Entropy And The Second Law: Interpretation And Misss-Interpretationsss ( https://www…

Thanks, I do appreciate you extracting this. I did follow one or two of these originally. But I'm not going to buy an ebook on Amazon to figure out if he has anything useful to say.

LibGen?

"Shannon's Measure of Information and the Thermodynamic Entropy" https://doi.org/10.1063/1.3703629

Re: Demystifying the second law of thermodynamics

#29

Post by zug_zug »

adeledeweylopez wrote: post #21
zug_zug wrote: post #16

There's something about attempts at entropy that feels entirely inadequate. The definition of "law" in science isn't something that's true, just something that we haven't observed any exceptions to (yet). However entropy, is in larger systems entirely unmeasurable as far as I understand (is there even a unit for it?). Rather than tackle-these scientific shortcomings head-on, most tend to gloss over it. Perhaps a good…

Entropy is a measure of the uncertainty that an observer has over the microstates (i.e. the exact state of every atom) given their knowledge of the macrostate (i.e. what they are capable of describing: like "the water is just above freezing"). So it's inherently a subjective concept. The most common unit for entropy is the bit, same unit as information. Anyway, entropy is measurable just like any other physical quant…

>> Anyway, entropy is measurable just like any other physical quantity

Uh, I measure the mass of a baseball by putting it on a scale, and I get an objective number in kilograms. Similar for velocity, temperature, and volume.

So far as I know, entropy is pretty unique in that there isn't, and will never be an instrument that gives the number of bits in a baseball.

>> So it's inherently a subjective concept.

Yes, this is my point. Almost nothing in physics is subjective.

Re: Demystifying the second law of thermodynamics

#30

Post by Geminidog »

SuoDuanDao wrote: post #11
zug_zug wrote: post #3

This is speaking of entropy and states of gasses. Isn't there some generalization of entropy, such that even when sentient life-forms tried their damnedest, or even in black-holes, entropy must always trend up? Or was that a mischaracterization?

Ask three thermodynamics engineers, get five answers. The generalization you're referring to is pretty accurate, but according to some interpretations it's just assumed to exist a priori and then we look for evidence of it. But while it's unclear whether entropy is the result of some universal law or a hack we use to make the math work out, it definitely does make the math work out in closed systems of gasses.

entropy is phenomenon of probability. It works because probability works.

People think entropy is some natural phenomenon in nature that is fundamental.

No. Entropy is a consequence of probability. The math works because probability happens to apply to nature. The below is the intuition behind why entropy occurs... once you will realize this it will make sense.

   Disordered states tend to be more numerous then ordered states that's why any random configuration of gas particles in a system is more likely to be disordered.

   Also when you try to purturb the state of random particles from state1 to state2, by probability state2 will be disordered because there are far more possible disordered states than ordered states... even when the initial state is ordered. Hence entropy increases.
The philosophical thing people should be examining is the nature of probability and reality which we already know is intrinsically tied with the nature of fundamental particles.

Probability is an axiom, entropy is a theorem derived from the axiom of probability.

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