Entropy - Revision history

Tom: /* Relevant vs. Irrelevant */

2024-12-25T05:20:46Z

‎Relevant vs. Irrelevant

Tom: /* Relevant vs. Irrelevant */

2024-12-25T05:19:09Z

‎Relevant vs. Irrelevant

Tom: /* Context */

2024-12-25T01:46:37Z

‎Context

Tom: /* Confronting Misuses of Entropy */

2024-10-22T22:45:16Z

‎Confronting Misuses of Entropy

Tom: /* Context */

2024-10-22T22:37:18Z

‎Context

Tom: /* Context */

2024-10-22T22:32:07Z

‎Context

Tom: /* Context */

2024-10-22T22:31:20Z

‎Context

Tom: /* Principle of Maximum Rate of Entropy Production */

2024-07-08T01:25:17Z

‎Principle of Maximum Rate of Entropy Production

Tom: /* Principle of Maximum Rate of Entropy Production */

2024-07-08T01:08:31Z

‎Principle of Maximum Rate of Entropy Production

Tom: /* Problems */

2024-07-08T01:04:14Z

‎Problems

@@ Line 36: / Line 36: @@
 given a system, entropy measures our ignorance in irrelevant quantities over relevant quantities
-What's even more interesting is that physics itself might be just a measure of what is relevant for humans.
+What's even more interesting is that physics itself might be just a measure of what is relevant for humans. A similar appraisal might be appropriate for measuring "useful" work, useful for who?
 ===Confronting Misuses of Entropy===

@@ Line 35: / Line 35: @@
 In summary, the more sophisticated definition of entropy is:
 given a system, entropy measures our ignorance in irrelevant quantities over relevant quantities
 ===Confronting Misuses of Entropy===
 Armed with our newfound understanding of entropy, let’s confront some common misuses of entropy. Say there is a huge mess on the floor. Is the entropy high or low? Does a messy floor imply a high entropy?

@@ Line 3: / Line 3: @@
 ==Context==
 * Entropy is often treated as synonymous to chaos and disorder. This page considers entropy to be the lack of information. Some of the structure of this section come from [https://medium.com/swlh/entropy-is-not-disorder-a-physicists-perspective-c0dccfea67f1 Entropy is not disorder: A physicist’s perspective]
 * The real progenitor for [[Entropy]] is the [[Second Law of Thermodynamics]] which has been characterized as foretelling the heat death of the universe.

@@ Line 35: / Line 35: @@
 given a system, entropy measures our ignorance in irrelevant quantities over relevant quantities
 ===Confronting Misuses of Entropy===
-Armed with our newfound understanding of entropy, let’s confront some common misuses of entropy. Say there is a huge mess on the floor like the picture below. Is the entropy high or low?
+Armed with our newfound understanding of entropy, let’s confront some common misuses of entropy. Say there is a huge mess on the floor. Is the entropy high or low? Does a messy floor imply a high entropy?
 Well, that is a trick question! Just like the digits of pi example I showed above, the question is ill-defined. We simply cannot compute an entropy meaningfully until we know what the relevant and irrelevant variables are! Indeed, the mess on the floor could be a delicate piece of art, and who’s to say a particular splotch of paint wasn’t the result of a carefully planned masterpiece?
-Here’s another common misuse. Say my ceramics fell on the floor. Did entropy increase? Did entropy increase because a piece of ceramics fell onto the ground?
+Here’s another common misuse. Say my ceramics fell on the floor. Did entropy increase? Did entropy increase because a piece of ceramics fell onto the ground? The answer is probably yes, but not because the pieces seem to be arranged in a more chaotic way. Entropy is always increasing in daily physical processes. The fact that the pieces of ceramics are separated instead of stuck together doesn’t contribute much to the notion of entropy.
 Let’s think back to the previous discussion on relevant vs. irrelevant quantities. Are the ceramic pieces rapidly changing and rearranging in such a way that the system thermalizes? No. So, it doesn’t make a lot of sense to associate entropy with the patterns of broken pieces of ceramics.
 If we were to imagine some weird simulation where the exact same piece of ceramics is breaking over and over again and we want to pretend that there is some sort of thermalization process, we could try to create some notion of entropy, but it would be a weird ad-hoc notion at best.
 So, we now know that entropy doesn’t capture some objective, fundamental notion of disorder. Why, then, do we associate entropy with chaos and disorder?
 ===Relationship to statistics and information===
 To get a better understanding, we need to make a connection to statistics. Given a probability distribution p, we can compute a quantity called the information entropy H. The information entropy measures how random the given probability distribution is. It is given by

@@ Line 5: / Line 5: @@
 * Entropy is often treated as synonymous to chaos and disorder. This page considers entropy to be the lack of information. Some of the structure of this section come from [https://medium.com/swlh/entropy-is-not-disorder-a-physicists-perspective-c0dccfea67f1 Entropy is not disorder: A physicist’s perspective]
 * The real progenitor for [[Entropy]] is the [[Second Law of Thermodynamics]] which has been characterized as foretelling the heat death of the universe.
-* The fact that [[Entropy]] has been low in the past leads to the observation that relics of the past exist in the present, while the future is unknowable to us mere mortals.
+* The fact that [[Entropy]] has been low in the past leads to the observation that relics of the past exist in the present, while the future is unknowable to us mere mortals. In order to leave a trace, the events of the past must have been frozen in-place. This can only happen in irreversible processes, which, once frozen, cannot be undone.
 * The real paradox is the struggle between order and chaos - between the [[Doing and Undoing]].

@@ Line 78: / Line 78: @@
 research.<ref>Jim Al-Khalili and Eddy Keming Chen, ''The Decoherent Arrow of Time and the Entanglement Past Hypothesis'' 2024-05-07 https://philpapers.org/archive/ALKTDA.pdf</ref>
 ==Principle of Maximum Rate of Entropy Production==
-Garth W. Paltridge researched topics such as the optimum design of plants and the economics of climate forecasting, and worked on atmospheric radiation and the theoretical basis of climate. Paltridge introduced the subsequently disputed hypothesis that the earth/atmosphere climate system adopts a format that maximizes its rate of thermodynamic dissipation, i.e., entropy production. This suggests a governing constraint by a principle of maximum rate of entropy production. According to this principle, prediction of the broad-scale steady-state distribution of cloud, temperature and energy flows in the ocean and atmosphere may be possible when one has sufficient data about the system for that purpose, but does not have fully detailed data about every variable of the system.<ref>G. W.  Paltridge, ''The steady-state format of global climate''. Quarterly Journal of the Royal Meteorological Society. 104 (442): 927–945.(1978) Bibcode:1978QJRMS.104..927P. doi:10.1002/qj.49710444206.</ref>
+Garth W. Paltridge researched topics such as the optimum design of plants and the economics of climate forecasting, and worked on atmospheric radiation and the theoretical basis of climate. Paltridge introduced the subsequently disputed hypothesis that the earth/atmosphere climate system adopts a format that maximizes its rate of thermodynamic dissipation, i.e., entropy production. This suggests a governing constraint by a principle of maximum rate of entropy production. According to this principle, prediction of the broad-scale steady-state distribution of cloud, temperature and energy flows in the ocean and atmosphere may be possible when one has sufficient data about the system for that purpose, but does not have fully detailed data about every variable of the system.<ref>G. W.  Paltridge, ''The steady-state format of global climate''. Quarterly Journal of the Royal Meteorological Society. 104 (442): 927–945.(1978) Bibcode:1978QJRMS.104..927P. doi:10.1002/qj.49710444206.</ref> This principle served as the basis for Tim Palmer to switch from [[Physics]] to Meteorology with the idea that this might turn into a fantastic unifying principle.<ref name="palmer">Tim Palmer, ''The Primacy of Doubt'', (2022)  ISBN 9781541619715</ref>
 ==References==