Entropy and information: Do physicists still believe so?

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Discussion Overview

The discussion revolves around the relationship between entropy and information, particularly in the context of statistical mechanics and the concept of Maxwell's demon. Participants explore how acquiring information about microstates affects entropy and whether this aligns with classical and quantum interpretations of entropy.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested

Main Points Raised

  • Some participants propose that knowing the microstates of a system decreases the number of accessible states, thereby reducing entropy, as expressed by the equation S = k*ln W.
  • Others argue that while acquiring information about microstates can conceptually lower entropy, the practical implications are negligible for large systems due to the vast amount of information required.
  • A participant introduces the idea of Maxwell's demon, suggesting that if one could control the movement of particles using microstate information, it might allow for a return to a lower-entropy state without additional entropy cost.
  • Another participant questions whether the act of acquiring information itself increases entropy, leading to a discussion about the role of erasing information in increasing entropy by a specific amount (kb ln 2).
  • There is mention of reversible computing as a field that studies information processing without erasure, which could have implications for energy consumption and quantum computing.
  • Participants discuss the historical context of the Maxwell's demon paradox and its resolution, with some disagreement on the timeline of key publications related to the topic.

Areas of Agreement / Disagreement

Participants express differing views on the implications of information acquisition for entropy, with no consensus on whether the act of acquiring information increases entropy or how it relates to the concept of Maxwell's demon. The discussion remains unresolved regarding the practical effects of these theories.

Contextual Notes

Limitations include the dependence on definitions of entropy and microstates, as well as the unresolved nature of how information acquisition interacts with entropy in practical scenarios.

LTP
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The entropy of a system is
S = k*ln W
If we obtain some information about the microstates, e.g. know the location and velocities of some of the molecules, then W is decreased by a amount w, so
S1 = k*ln(W-w)
That is an decrease in entropy, i.e. S1 < S.

Do physicists still "believe" so?
 
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LTP said:
The entropy of a system is
S = k*ln W
If we obtain some information about the microstates, e.g. know the location and velocities of some of the molecules, then W is decreased by a amount w, so
S1 = k*ln(W-w)
That is an decrease in entropy, i.e. S1 < S.

Do physicists still "believe" so?

Yes, at least for von Neumann entropy. The point is that to "know" this microstate information, means that you've limited the number of states the system can be in because now it are those microstates that are compatible with your information: the only way to know that information, is by forcing it somehow in a subset of states.
In practice this doesn't make any difference, because for a statistically significant number of particles (from the moment it starts making sense doing thermodynamics), the amount of knowledge you'd need to gather is so huge before it starts influencing the numerical value of entropy, that it is not feasible.

The reason why this lowers entropy is that you can USE that information to go to a "real" lower-entropy state.

Imagine a gas in a box, which is a mixture of two components A and B. Now, you know that the entropy of this mixture is higher than if component A was in the left half of the box and component B in the right half (eventually with a wall in between). It is the entropy of mixture.
But imagine that somehow, we know all the microstates of motion of all the particles A and B. Imagine that we have still a wall in the box, but this time with a tiny shutter. We could use all that information to pilot the "Maxwell demon", each time we KNOW that a molecule A is going to the left, or a molecule B is going to the right.
So we could go back to the state before the mixture, without (with an ideal demon) spending any "entropy" elsewhere.
 
Last edited:
vanesch said:
Yes, at least for von Neumann entropy.
But also in "classical" entropy?

vanesch said:
Imagine a gas in a box, which is a mixture of two components A and B. Now, you know that the entropy of this mixture is higher than if component A was in the left half of the box and component B in the right half (eventually with a wall in between). It is the entropy of mixture.
But imagine that somehow, we know all the microstates of motion of all the particles A and B. Imagine that we have still a wall in the box, but this time with a tiny shutter. We could use all that information to pilot the "Maxwell demon", each time we KNOW that a molecule A is going to the left, or a molecule B is going to the right.
So we could go back to the state before the mixture, without (with an ideal demon) spending any "entropy" elsewhere.
So what is preventing us from being such a demon? Do you imply that the act of information acquisition increases the entropy?
 
LTP said:
So what is preventing us from being such a demon? Do you imply that the act of information acquisition increases the entropy?

No, as it turns out it is the act of ERASING information that increases the entropy by an amount kb ln 2. This can actually be shown experimentally. There is a whole field called "reversible computing" where people study circuits where information is never erased which actually reduces the energy consumption somewhat.
It is also a field that has become increasingly important over the past decade or so since it turns out that quantum computers must be reversible in order to work; meaning many results from reversible computing are also applicable also to quantum computing.

The "Maxwell's demon" paradox was one of the great unsolved mysteries in physics until it was solved about 80 years ago.
 
f95toli said:
No, as it turns out it is the act of ERASING information that increases the entropy by an amount kb ln 2.
I agree.

f95toli said:
This can actually be shown experimentally.
Really? - How? AFAIK "normal" computers don't come anywhere near that lower limit.
f95toli said:
The "Maxwell's demon" paradox was one of the great unsolved mysteries in physics until it was solved about 80 years ago.
More likely 40 years, Landauer published his paper in 1961, Bennett published his solution to MS in the same decade.
 

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