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What is entropy? A measure of just how little we know

quantamagazine.org

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Re: What is entropy? A measure of just how little we know

#51

Post by kgwgk »

kergonath wrote: post #31
kqr wrote: post #2

> As physicists have worked to unite seemingly disparate fields over the past century, they have cast entropy in a new light — turning the microscope back on the seer and shifting the notion of disorder to one of ignorance. Entropy is seen not as a property intrinsic to a system but as one that’s relative to an observer who interacts with that system. Maybe I have the benefit of giant shoulders, but this seems like a…

> Maybe I have the benefit of giant shoulders, but this seems like a fairly mundane observation. It is not mundane, and it is also not right, at least for entropy in Physics and Thermodynamics. > High-entropy states are those macrostates which have many corresponding microstates. That is how you deduce entropy form a given model. But entropy is also something that we can get from experimental measurements. In this ca…

> But entropy is also something that we can get from experimental measurements. In this case, the experimental setup does not care about microstates and macrostates, it just has properties like enthalpy, heat capacity and temperature. […] experimental measurements of the entropy of a given materials are consistent and independent of whatever model the people doing the experiment were operating on. Fundamentally, entropy depends on the probability distribution, not the observer.

https://bayes.wustl.edu/etj/articles/gibbs.vs.boltzmann.pdf

Thermodynamics does have the concept of the entropy of a thermodynamic system; but a given physical system corresponds to many different thermodynamic systems. […] It is clearly meaningless to ask, “What is the entropy of the crystal?” unless we first specify the set of parameters which define its thermodynamic state. […] There is no end to this search for the ultimate "true" entropy until we have reached the point where we control the location of each atom independently. But just at that point the notion of entropy collapses, and we are no longer talking thermodynamics! […] From this we see that entropy is an anthropomorphic concept, not only in the well-known statistical sense that it measures the extent of human ignorance as to the microstate. Even at the purely phenomenological level, entropy is an anthropomorphic concept. For it is a property, not of the physical system, but of the particular experiments you or I choose to perform on it.

Re: What is entropy? A measure of just how little we know

#52

Post by j7ake »

amelius wrote: post #35

Makes sense. If we knew the theory of everything and the initial conditions of the universe, then we could just compute the next episode of a series instead of streaming it.

Try it with a chaotic system like a double pendulum you’ll see the dynamics are not predictive in the long term.

Re: What is entropy? A measure of just how little we know

#53

Post by adrianN »

j7ake wrote: post #52
amelius wrote: post #35

Makes sense. If we knew the theory of everything and the initial conditions of the universe, then we could just compute the next episode of a series instead of streaming it.

Try it with a chaotic system like a double pendulum you’ll see the dynamics are not predictive in the long term.

Is that true? It was my understanding that chaotic systems (with a known initial state) could be predicted to arbitrary precision by throwing enough compute at the problem. Of course knowing the initial state is impossible in the real world, „enough“ compute might not fit in the observable universe, and quantum mechanics contains true randomness…

Re: What is entropy? A measure of just how little we know

#54

Post by bubblyworld »

niemandhier wrote: post #33
bubblyworld wrote: post #9

Earlier quoted context omitted.

I think you may have misunderstood the OP's point - the entropy you calculate for a system depends on how you factor the system into micro and macro states. This doesn't really have anything to do with changes of reference frame - in practice it's more about limitations on the kinds of measurements you can make of the system. (you can't measure the individual states of all the particles in a body of gas, for instance…

From a thermodynamics point of view only the differential of the entropy matters, so if there is only a fixed difference between the two computations they do not influence the physics. If the way one does the coarse graining of states results in different differentials, one way should be the correct one. There is only one physics. If I remember one of Plancks relevations was that he could explain why a certain correc…

That's true - for instance I believe many of the results of statistical mechanics rely on further assumptions about your choice of macrostates, like the fact that they are ergodic (i.e. the system visits each microstate within a macrostate with equal probability on average). Obviously exotic choices of macrostates will violate these assumptions, and so I would expect the predictions such a model makes to be incorrect.

But ultimately that's an empirical question. Entropy is a more general concept that's definable regardless of whether the model is accurate or not.

Re: What is entropy? A measure of just how little we know

#55

Post by philipov »

adrianN wrote: post #53
j7ake wrote: post #52

Earlier quoted context omitted.

Try it with a chaotic system like a double pendulum you’ll see the dynamics are not predictive in the long term.

Is that true? It was my understanding that chaotic systems (with a known initial state) could be predicted to arbitrary precision by throwing enough compute at the problem. Of course knowing the initial state is impossible in the real world, „enough“ compute might not fit in the observable universe, and quantum mechanics contains true randomness…

Yes, chaotic systems can be simulated, and that's the only way to find out what happens with them. The thing one can't do is reduce them to a closed-form function of x and compute their value for any point along their domain. The only thing we can do is inductively figure out the next x from the current x.

Re: What is entropy? A measure of just how little we know

#56

Post by ziofill »

Very nice article. There’s an alternative way of thinking of the Gibbs paradox, which is to attach labels to the particles. This naturally makes them distinguishable and increases the total number of possible configurations, and with it the maximum value of the entropy.

Re: What is entropy? A measure of just how little we know

#57

Post by ganzuul »

Trasmatta wrote: post #48
noiv wrote: post #44

What about the efficiency to remove entropy? Is there a threshold our combined efforts called science cannot surpass? Do we need Frank Herbert’s spice to progress?

A localized reduction of entropy will always result in an increase of entropy in the larger system. It doesn't matter how efficient your process is, the entropy of the surrounding system will ALWAYS increase as the result of the work needed to effect a localized reduction.

Unless the surrounding system is already at infinite entropy.

Re: What is entropy? A measure of just how little we know

#58

Post by markisus »

daoboy wrote: post #20

The interactive graphic that tries to show entropy is subjective doesn't sit right for me. They fail to properly define the macrostate of the system under consideration, then show two different observed entropies for two different macrostates (Colors for Alice and Shapes for Bob). That doesn't show entropy is subjective, it shows that defining the system is subjective. The same two macrostates would still have the sa…

Maybe if you take Alice and Bob to be two separate alien species it could make more sense. Alice’s species has no measurement devices capable of detecting Bob’s version of entropy, and therefore Alice is not able to extract any useful work from Bob’s system and vice versa. Therefore any objective definition of entropy needs to include the capabilities of the measurer. Which is just the same as what you were saying about macrostates.

Re: What is entropy? A measure of just how little we know

#60

Post by revskill »

plank wrote: post #26

Interesting to read this, 27 years after my PhD* (theoretical physics), in which I did compare the view WITH and the view WITHOUT ‘unknowns’ causing entropy as a driver. * My PhD was about how to treat a (quantum mechanical) system inside a cavity: a cavity with one perfect mirror and one 99.999999% perfect mirror. The (one dimensional) universe was made whole by another perfect mirror at the other side of the non-pe…

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