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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

#101

Post by monadINtop »

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.

a theory of everything would have to have quantum mechanics as an emergent theory and quantum mechanics is fundamentally non-deterministic. and even if it was, a theory of everything is almost certainly not going to be practically computable for the same reason that even basic non-relativistic quantum mechanics cannot even solve for a reasonably sized molecule numerically (let alone exactly - just as classical mechanics is unsolvable for more than two bodies)

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

#102

Post by pixl97 »

whatshisface wrote: post #100
kergonath wrote: post #90

Earlier quoted context omitted.

> The enthalpy changes measured by a calorimeter are dependent on the design of the calorimeter, which could have been a different piece of equipment. Right, but that is true of anything. Measuring devices need to be calibrated and maintained properly. It does not make something like a distance subjective, just because someone is measuring it in cm and someone else in km. > If you introduced a new bit of macro inform…

Entropy isn't subjective, but it is relative to what you can measure about a given system, or what measurements you are analyzing a system with respect to. In quantum mechanics there are degenerate ground states, and in classical mechanics there are cases where the individual objects (such as stars) are visible but averaged over. You should take a look at the Gibbs paradox.

I would say an even more limiting measure of entropy shows that entropy isn't subjective. That is entropy is the ability to extract useful work from a system by moving the system from a state of lower entropy to a state of higher entropy (in a closed system)

No subjective measure of entropy can allow you to create a perpetual motion machine. The measurements of any two separate closed systems could be arbitrary, but when said systems are compared with each other units and measurements standardize.

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

#103

Post by kgwgk »

pixl97 wrote: post #102
whatshisface wrote: post #100

Earlier quoted context omitted.

Entropy isn't subjective, but it is relative to what you can measure about a given system, or what measurements you are analyzing a system with respect to. In quantum mechanics there are degenerate ground states, and in classical mechanics there are cases where the individual objects (such as stars) are visible but averaged over. You should take a look at the Gibbs paradox.

I would say an even more limiting measure of entropy shows that entropy isn't subjective. That is entropy is the ability to extract useful work from a system by moving the system from a state of lower entropy to a state of higher entropy (in a closed system) No subjective measure of entropy can allow you to create a perpetual motion machine. The measurements of any two separate closed systems could be arbitrary, but…

> entropy is the ability to extract useful work from a system

https://www.damtp.cam.ac.uk/user/tong/statphys/jaynes.pdf

The amount of useful work that we can extract from any system depends - obviously and necessarily - on how much “subjective” information we have about its microstate, because that tells us which interactions will extract energy and which will not; this is not a paradox, but a platitude. If the entropy we ascribe to a macrostate did not represent some kind of human information about the underlying microstates, it could not perform its thermodynamic function of determining the amount of work that can be extracted reproducibly from that macrostate. […] the rules of thermodynamics are valid and correctly describe the measurements that it is possible to make by manipulating the macro variables within the set that we have chosen to use. This useful versatility - a direct result of and illustration of the “anthropomorphic” nature of entropy - would not be apparent to, and perhaps not believed by, someone who thought that entropy was, like energy, a physical property of the microstate.

Edit: I’ve just noticed that the article discussed links to this paper, and quotes the first sentence above, and details the whifnium example given in the […] above.

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

#104

Post by pixl97 »

tsoukase wrote: post #13

My perspective: 1) entropy is a mathematical concept. Physics apply it, like any other mathematical one 2) math entropy does not change, everything is reversible, as it is based on known quantities 3) entropy measures how far we are from perfectly knowing a system 4) logarithm is chosen to measure entropy because of its convenient properties, not because of any deeper law. It could be a sum, a product etc 5) the Seco…

5) there is no every system, there is only the universe in which all systems increase in entropy even if individual objects (block of ice) do not. You're bleeding off entropy into the universe you can never get back.

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

#105

Post by UltraSane »

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…

> That’s how we say that e.g. hydrogen atoms are indistinguishable. It’s not that they become indistinguishable because we decide so. It’s because we can calculate entropy in both cases and reality does not match the model with distinguishable atoms.

How does using isotopes that allow atoms to be distinguished affect entropy?

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

#106

Post by Jensson »

kgwgk wrote: post #51
kergonath wrote: post #31

Earlier quoted context omitted.

> 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, entr…

Temperature is not just an anthropomorphic concept, and temperature and entropy are directly linked concept you can't have one without the other.

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

#107

Post by kgwgk »

pixl97 wrote: post #104
tsoukase wrote: post #13

My perspective: 1) entropy is a mathematical concept. Physics apply it, like any other mathematical one 2) math entropy does not change, everything is reversible, as it is based on known quantities 3) entropy measures how far we are from perfectly knowing a system 4) logarithm is chosen to measure entropy because of its convenient properties, not because of any deeper law. It could be a sum, a product etc 5) the Seco…

5) there is no every system, there is only the universe in which all systems increase in entropy even if individual objects (block of ice) do not. You're bleeding off entropy into the universe you can never get back.

In classical thermodynamics, the entropy of a system is defined if and only if it is in a thermodynamic equilibrium.

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

#109

Post by foobarbecue »

UltraSane wrote: post #105
kergonath wrote: post #31

Earlier quoted context omitted.

> 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…

> That’s how we say that e.g. hydrogen atoms are indistinguishable. It’s not that they become indistinguishable because we decide so. It’s because we can calculate entropy in both cases and reality does not match the model with distinguishable atoms. How does using isotopes that allow atoms to be distinguished affect entropy?

Add more particles, get more possible states. Hydrogen is a proton and an electron. Deuterium adds a neutron. More possible states means more entropy, assuming your knowledge of the system stayed constant.

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

#110

Post by [deleted] »

Jensson wrote: post #106
kgwgk wrote: post #51

Earlier quoted context omitted.

> 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, entr…

Temperature is not just an anthropomorphic concept, and temperature and entropy are directly linked concept you can't have one without the other.

[deleted]
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