6 ms·

> there are far more ways for a system to be disordered than ordered I'm a complete layman when it comes to physics, so forgive me if this is naive — but aren'

by ludwik 1y ago

> there are far more ways for a system to be disordered than ordered I'm a complete layman when it comes to physics, so forgive me if this is naive — but aren't "ordered" and "disordered" concepts tied to human perception or cognition? It always seemed to me that we call something "ordered" when we can find a pattern in it, and "disordered" when we can't. Different people or cultures might be able to recognize patterns in different states. So while I agree that "there are more ways for a system to be disordered than ordered," I would have thought that's a property of how humans perceive the world, not necessarily a fundamental truth about the universe

hackinthebochs 1y ago
Think minimum description length. Low entropy states require fewer terms to fully describe than high entropy states. This is an objective property of the system.
- amelius 1y ago
  In a deterministic system you can just use the time as a way to describe a state, if you started from a known state.
- sat_solver 1y ago
  You're thinking of information entropy, which is not the same concept as entropy in physics. An ice cube in a warm room can be described using a minimum description length as "ice cube in a warm room" (or a crystal structure inside a fluid space), but if you wait until the heat death of the universe, you just have "a warm room" (a smooth fluid space), which will have an even shorter mdl. Von Neuman should never have repurposed the term entropy from physics. Entropy confuses a lot of people, including me.
  - nick__m 1y ago
    And somewhat surprisingly the heat death of the universe is the maximal entropy state. Because there are an infinite number of microstates (all the particles are interchangeable) that lead to the same macrostate: nothing happening for ever!
  - hackinthebochs 1y ago
    Maxwell's demon thought experiment implies they are the same concept. Given a complete knowledge of every particle of gas you can in principle create unphysical low entropy distributions of the particles. This[1] goes into more detail. [1] https://en.wikipedia.org/wiki/Entropy_in_thermodynamics_and_information_theory#Information_is_physical https://en.wikipedia.org/wiki/Entropy_in_thermodynamics_and_...
    - bavell 1y ago
      A fun visual explanation: https://youtu.be/8Uilw9t-syQ?si=D9sR2YAm40SPFG3a https://youtu.be/8Uilw9t-syQ?si=D9sR2YAm40SPFG3a
- zmgsabst 1y ago
  “Number of terms” is a human language construct.
  - hackinthebochs 1y ago
    No, it's a representation construct, i.e. how to describe some system in a given basis. The basis can be mathematical. Fourier coefficients for example.
    - zmgsabst 1y ago
      Mathematics is a human language. It being a formal language doesn’t change that. Further, it’s not objective: you’re choosing the basis which causes the complexity, but any particular structure can be made simple in some basis.
      - hackinthebochs 1y ago
        Mathematical notation is a human invention, but the structure that mathematics describes is objective. The choice of basis changes the absolute number of terms, but the relative magnitude of terms for a more or less disordered state is generally fixed outside of degenerate cases.
        zmgsabst 1y ago
        The structure that most words describe is objective, so you haven’t distinguished math as a language. (Nor is mathematics entirely “objective”, eg, axiom of choice.) And the number of terms in your chosen language with your chosen basis isn’t objective: that’s an intrinsic fact to your frame. The complexity of terms is not fixed — that’s simply wrong mathematically. They’re dependent on our chosen basis. Your definition is circular, in that you’re implicitly defining “non-degenerate” as those which make your claim true. You can’t make the whole class simplified at once, but for any state, there exists a basis in which it is simple.
        1y ago
mr_mitm 1y ago
You only hear these terms in layman explanations. Physics has precise definitions for these things. When we say "ordered", we mean that a particular macrostate has only few possible microstates. Check this Wikipedia article for a quick overview: https://en.wikipedia.org/wiki/Microstate_(statistical_mechanics) https://en.wikipedia.org/wiki/Microstate_(statistical_mechan... Details can be found in any textbook on statistical mechanics.
- Gravityloss 1y ago
  Exactly. The coin flipping example is a very nice way to put it. It works since the coins are interchangeable, you just count the number of heads or tails. If the coins were of different color and you took that into account, then it wouldn't work. It's not intuitive to me what gravity has to do with entropy though, as it's classically just a force and completely reversible (unlike entropy)? Ie if you saw a video of undisturbed objects only affected by gravity, you couldn't tell if the video was reversed.
  - floxy 1y ago
    > Ie if you saw a video of undisturbed objects only affected by gravity, you couldn't tell if the video was reversed. How does that work with things like black holes? If you saw an apple spiral out of a black hole, wouldn't you suspect that you were watching a reversed video? Even if you take account the gravitational waves?
    - kgwgk 1y ago
      If you saw a comet coming from the sun, or a meteorite coming from the moon, etc. you would also find that suspicious.
      - Gravityloss 1y ago
        Comets are in elliptical orbits around the sun so literally half the time they're traveling away from the sun.
spyrja 1y ago
You can safely replace the terms "order" and "disorder" with "unlikely" and "likely". Simply put, entropy is a measure of how closely a system resembles its "most likely configuration". Consider the discrete entropy of a series of coin flips. Three tosses could result in the following 8 states: HHH, HHT, HTH, HTT, THH, THT, TTH, and TTT. From that we can gather that there is a 1/8 chance of getting either zero or three heads and a 3/8 chance of getting one or two heads. That latter two cases are clearly more likely (and hence associated with a higher entropy). In physics of course entropy is generally the continuous kind, not simple set of binary microstates. But the principle is essentially the same.

by ludwik 1y ago

hackinthebochs 1y ago

Think minimum description length. Low entropy states require fewer terms to fully describe than high entropy states. This is an objective property of the system.

amelius 1y ago
In a deterministic system you can just use the time as a way to describe a state, if you started from a known state.
sat_solver 1y ago
You're thinking of information entropy, which is not the same concept as entropy in physics. An ice cube in a warm room can be described using a minimum description length as "ice cube in a warm room" (or a crystal structure inside a fluid space), but if you wait until the heat death of the universe, you just have "a warm room" (a smooth fluid space), which will have an even shorter mdl. Von Neuman should never have repurposed the term entropy from physics. Entropy confuses a lot of people, including me.
- nick__m 1y ago
  And somewhat surprisingly the heat death of the universe is the maximal entropy state. Because there are an infinite number of microstates (all the particles are interchangeable) that lead to the same macrostate: nothing happening for ever!
- hackinthebochs 1y ago
  Maxwell's demon thought experiment implies they are the same concept. Given a complete knowledge of every particle of gas you can in principle create unphysical low entropy distributions of the particles. This[1] goes into more detail. [1] https://en.wikipedia.org/wiki/Entropy_in_thermodynamics_and_information_theory#Information_is_physical https://en.wikipedia.org/wiki/Entropy_in_thermodynamics_and_...
  - bavell 1y ago
    A fun visual explanation: https://youtu.be/8Uilw9t-syQ?si=D9sR2YAm40SPFG3a https://youtu.be/8Uilw9t-syQ?si=D9sR2YAm40SPFG3a
zmgsabst 1y ago
“Number of terms” is a human language construct.
- hackinthebochs 1y ago
  No, it's a representation construct, i.e. how to describe some system in a given basis. The basis can be mathematical. Fourier coefficients for example.
  - zmgsabst 1y ago
    Mathematics is a human language. It being a formal language doesn’t change that. Further, it’s not objective: you’re choosing the basis which causes the complexity, but any particular structure can be made simple in some basis.
    - hackinthebochs 1y ago
      Mathematical notation is a human invention, but the structure that mathematics describes is objective. The choice of basis changes the absolute number of terms, but the relative magnitude of terms for a more or less disordered state is generally fixed outside of degenerate cases.
      - zmgsabst 1y ago
        The structure that most words describe is objective, so you haven’t distinguished math as a language. (Nor is mathematics entirely “objective”, eg, axiom of choice.) And the number of terms in your chosen language with your chosen basis isn’t objective: that’s an intrinsic fact to your frame. The complexity of terms is not fixed — that’s simply wrong mathematically. They’re dependent on our chosen basis. Your definition is circular, in that you’re implicitly defining “non-degenerate” as those which make your claim true. You can’t make the whole class simplified at once, but for any state, there exists a basis in which it is simple.
        1y ago

mr_mitm 1y ago

You only hear these terms in layman explanations. Physics has precise definitions for these things. When we say "ordered", we mean that a particular macrostate has only few possible microstates. Check this Wikipedia article for a quick overview: https://en.wikipedia.org/wiki/Microstate_(statistical_mechanics) https://en.wikipedia.org/wiki/Microstate_(statistical_mechan... Details can be found in any textbook on statistical mechanics.

Gravityloss 1y ago
Exactly. The coin flipping example is a very nice way to put it. It works since the coins are interchangeable, you just count the number of heads or tails. If the coins were of different color and you took that into account, then it wouldn't work. It's not intuitive to me what gravity has to do with entropy though, as it's classically just a force and completely reversible (unlike entropy)? Ie if you saw a video of undisturbed objects only affected by gravity, you couldn't tell if the video was reversed.
- floxy 1y ago
  > Ie if you saw a video of undisturbed objects only affected by gravity, you couldn't tell if the video was reversed. How does that work with things like black holes? If you saw an apple spiral out of a black hole, wouldn't you suspect that you were watching a reversed video? Even if you take account the gravitational waves?
  - kgwgk 1y ago
    If you saw a comet coming from the sun, or a meteorite coming from the moon, etc. you would also find that suspicious.
    - Gravityloss 1y ago
      Comets are in elliptical orbits around the sun so literally half the time they're traveling away from the sun.

spyrja 1y ago

You can safely replace the terms "order" and "disorder" with "unlikely" and "likely". Simply put, entropy is a measure of how closely a system resembles its "most likely configuration". Consider the discrete entropy of a series of coin flips. Three tosses could result in the following 8 states: HHH, HHT, HTH, HTT, THH, THT, TTH, and TTT. From that we can gather that there is a 1/8 chance of getting either zero or three heads and a 3/8 chance of getting one or two heads. That latter two cases are clearly more likely (and hence associated with a higher entropy). In physics of course entropy is generally the continuous kind, not simple set of binary microstates. But the principle is essentially the same.