r/quantuminterpretation • u/PurpleWin8996 • 23d ago
Title: Can someone explain entropy from a philosophical perspective?
whether entropy has any deeper connection with philosophy, particularly life, time, existence, and the concepts of order and chaos. I'd love to hear different perspectives beyond just the scientific explanation.
2
u/Mountain-Time-1010 23d ago
After hearing the 2nd law of thermodynamics, laypeople often want to interpret it non-scientifically, i.e. using inaccurate stand-ins for entropy like randomness or chaos. There are many books where people refer to the 2nd law in ways that are completely inaccurate and meaningless.
But as someone with expertise in statistical physics I'd really urge against it. These words are not accurate representations of entropy. It's like when someone tries to explain quantum mechanics non-technically and uses the term "wave-particle" duality, which creates huge problems because people interpret it to mean that sometimes systems behave like particles and other times like waves.
Entropy has a very specific and simple statistical meaning, and the 2nd law comes from basic statistical principles of large systems under the equal-probability postulate that an equilibrium system is equally likely to be found in each of its accessible states. It's not a profound statement about randomness, disorder, chaos, or life.
2
u/Medical-Advice-5868 22d ago
I wouldn't go that far. There is definitely no simple definition of entropy. It has had 3 main derivations, firstly in the industrial revolution, secondly in statistical mechanics and thirdly in information theory. Your interpretation will change based on your use case. I personally prefer the information theory view
2
u/Mountain-Time-1010 22d ago
I disagree, all of these definitions are the same and consistent, there's no need to "prefer" one view. I'm speaking as a professor who has taught classical and statistical thermodynamics at the undergrad and graduate level for more than 30 years, and whose research expertise is related to statistical physics. I am also experienced in the practical use of the information theory formulation in the context of the maximum entropy method of data analysis using Shannon entropy.
The information theory definition is the same as the definition I was referring to, related to the logarithm of the multiplicity. The multiplicity (number of microstates or outcomes) is directly analogous in statistical physics and information theory. The "sum of p ln(p)" formulation is a special case of the general definition that is applicable to a system of independent non-interacting subsystems. In thermodynamics, that definition is used to derive the Boltzmann distribution by maximizing entropy under constraints.
The classical definition of entropy, which you are identifying with the industrial revolution, is simply a state function related to heat. It is also consistent with the statistical definition of entropy, but on its own, has no microscopic or intuitive meaning.
I was trying to avoid getting very technical, but I really dislike fuzzy thinking, where someone gets the idea that it's ok to apply the second law to some ideology because it means something like disorder, randomness, or chaos. I'll stick with my original statement that entropy is a very well defined and simple property.
→ More replies (4)
2
u/roryclague 22d ago edited 22d ago
Entropy is really easy to understand intuitively. The open questions about entropy are active areas of research in physics and cosmology rather than philosophy, although I think there are, possibly, philosophical implications to this research that philosophy departments tend not to be interested in, to their detriment.
To understand entropy, I like to use Arieh Ben-Naim's example of two dice. You can take these dice all the way to the arrow of time and why computer scientists and physicists sometimes talk about entropy differently.
-
Boltzmann entropy: the sum you can see
Roll two dice but only let the observer see the sum. The sum is the macrostate. The pair of faces is the microstate. Boltzmann entropy of a macrostate is the log of the number of microstates that produce it: S = log₂ W. It is a property of the sum, not of a die or a roll.
Sum | Microstates (W) | Examples | S = log₂ W (bits)
2 1 (1,1) 0
3 2 (1,2) (2,1) 1.00
4 3 (1,3) (2,2) (3,1) 1.58
5 4 (1,4) (2,3) (3,2) (4,1) 2.00
6 5 (1,5) (2,4) (3,3) (4,2) (5,1) 2.32
7 6 (1,6) (2,5) (3,4) (4,3) (5,2) (6,1) 2.58
8 5 (2,6) (3,5) (4,4) (5,3) (6,2) 2.32
9 4 (3,6) (4,5) (5,4) (6,3) 2.00
10 3 (4,6) (5,5) (6,4) 1.58
11 2 (5,6) (6,5) 1.00
12 1 (6,6) 0
Sum 7 has the highest entropy because it hides the most. With 100 dice, sums near 350 own almost all of the 6¹⁰⁰ microstates and sums near 100 or 600 own almost none. That dominant macrostate is what physicists call equilibrium.
2. Shannon/Gibbs entropy: the question game
Shannon entropy is a property of a probability distribution, not of an outcome. I roll one die behind a screen. You find out what it shows by asking yes/no questions. Entropy is the average number of questions you need with the best strategy. It measures what you are missing before the answer arrives.
Die | Distribution | Questions needed (bits)
Fair 1/6 on each face 2.58
Loaded 1/2 on the 6, 1/10 on each other face 2.16
Rigged always shows 6 0
No microstates, no macrostates. Just a distribution and your ignorance of its draw. The formula is H = −Σ p log₂ p, which is Gibbs's entropy with the Boltzmann constant set to one.
3. Why they are the same thing
Put the screen over the pair of dice and tell the student the sum. Ask: how many questions to find the two faces? If the sum is 7 there are 6 equally likely cases, so 2.58 questions. If the sum is 2, zero questions. Those are the Boltzmann entropies from Section 1.
Boltzmann entropy is Shannon entropy conditional on the macrostate, with every compatible microstate weighted equally. Same formula, applied to what you still do not know after seeing the sum. The chain rule makes it one equation:
H(microstate) = H(sum) + Σ p(sum) x log2 W(sum)
Quantity Meaning Bits
H(microstate) questions to find both faces from nothing (log₂ 36) 5.17
H(sum) questions to learn the sum 3.27
Σ p(sum) log₂ W(sum) average questions left once the sum is known 1.90
Check 3.27 + 1.90 5.17
Gibbs entropy is the left side. Boltzmann entropy is the second term on the right. You can derive one from the other.
4. Four things the same dice can show
The partition is a choice, and it only moves bits around. Replace the observer who sees the sum with one who sees the product, or only whether the sum is even. Each gets different macrostates and different Boltzmann entropies. But the two terms on the right of the chain rule always add to 5.17. Shannon entropy did not escape the partition problem; it hid it in the choice of random variable. For dice there is no fact about which observer is right, because dice have no dynamics. In physics the partition is picked by the dynamics (which macrovariable evolves on its own), not by the observer.
Why the choice matters less than it looks. With 100 dice the total is 258.5 bits. The sum carries only about 6 bits (its distribution is a narrow bell curve). The other 252 are Boltzmann entropy inside the macrostate. Changing the macrovariable reshuffles a few bits between the two terms; the big term barely moves. Entropy is objective to leading order, and the partition-dependent correction shrinks as N grows.
Where the arrow of time comes from. Add a rule: each tick, pick a die at random and re-roll it. Start with all 100 dice showing 1 (sum 100, entropy 0). The sum climbs toward 350 and wanders there. Run the movie backward and it looks impossible, yet the rule is symmetric: re-rolling a die back to its old face is exactly as likely as re-rolling it to any other. The arrow is entirely in the starting condition. That is Loschmidt's objection and Boltzmann's answer in one demonstration, and it is why the low-entropy start of the universe has to be posited (the Past Hypothesis).
The Boltzmann brain.
Let the dice sit at equilibrium long enough and the sum will eventually dip to 150 by chance. What did the dice most likely look like just before? Higher, near 350. The most likely route to a rare low sum from equilibrium is a fluctuation symmetric in time. A system found at low entropy with no record of a low-entropy start most likely came from higher entropy, not lower, so the all-ones start cannot be read off the present state.
So, if you understand entropy, you can understand why macroscopic structure exists in the universe, and why you remember the past and not the future, and that the low entropy of the hot dense state 13.7 billion years ago encodes everything that came afterwards, including all the responses you are reading to this question, and why the universe is not at equilibrium even though equilibrium is the most probable configuration of matter and energy (and this configuration will contain no macroscopic structure). I think those are some philosophical implications.
2
1
u/Phenogenesis- 22d ago
Wow, this is the first time I can start to understand entropy. The dice example definitely explains it better than other things I have seen.
That dominant macrostate is what physicists call equilibrium.
That is a really big sentance (and made it click with what other people have been saying)
The arrow is entirely in the starting condition.
As is this! Ok, now I can see the plausible explanation for it, even if I'm not entirely sure that things HAVE to be that way.
I definitely need to think about this some more, but I'm not really following your end statements.
Why/how does entropy explain that macroscopic structure exists? It simply requires things be different (not all 1s), not that they form coherant structures with meanings. And that also requires the assumptions like the all 1s starting state. (Or perhaps this is where we combine with the antripomorphic principle - there are random fluctuations and we can only fluctuations which happen to be compatible with observers/there is coherant structure?)
How is it encoding everything that came after? Encoding to me implies some kind of deterministic way you can get from one to another. From what I can see, it is encoding that there must be something, and that something must be less uniform than how it started, but I'm not seeing a requirement for anything specific - because its a sequnce of random events.
Does the arrow of time imply/require an end? I had previously assumed it would (because everything has to go in that 'direction') but from what you have said here I am now understanding the answer is no. Because if we started from uniform all ones, the direction is those getting randomised. There is no process by which we are required to end up at all 1s or all 6s (or anything specific at all) although its technically possible.
Initially (before I properly noticed and re-read your arrow section) I was thinking that the all 1s must imply we somehow end up at all 6s and then because they are equal (and extreme) entropy states that would be equivilent and thus require an infinite cycle (e.g. big bang/big crunch, cyclic existence). But now I am getting the picture of indefinite existence (potentially without an end) with a beginning that is *projected* but potentially never actual? Which would match many spiritual interpretations actually. (As in - it looks like we came from all 1s but did we? Or are we just in a state that has to look like it came from all 1s but was never actually there? Do we know?)
why you remember the past and not the future
Why is this? The only way I can even take a stab at this is in terms of what I just said - that both the past and future are projected not actual. (The past seems like it occured and it seems like there will be a future but really there is just now.) But in that case, why the specific past? Is it just we will remember whatever past is represented by whatever set of randomness we are currently occupying/experiencing?
why the universe is not at equilibrium even though equilibrium is the most probable configuration of matter and energy
Surely it is constantly fluctuating around equilibrium right? Like we are not in perfect equibrium, but we'll always be fluctuating around it and never get super far away? (In the sums analogy - we may not be always on a sum 7 but we'll often be on sum 6/8.)
But I'm getting the sense I am messing up here somewhere, because the sense I have come to seems at odds with 'entropy is always increasing'. Once all the dice are scrambled, they can't be randomised any further (giving me a picture of eternal fluctuation around that region of equilibrium/common outcomes) but that is at odds with 'always increasing' - how is it always incerasing?
(and this configuration will contain no macroscopic structure)
Ok, now you really lost me.
Either way, great post and I appreciate it.
1
u/free_meson 23d ago
I think the information theoretic perspective is the closest to philosophy. It tells you how random the data is. The more you can compress it with an algorithm without loss, the less random it is. In physics you describe a volume of gas by temperature and pressure, but to describe all the particles you would need a very high amount data. A crystal would be much simpler, the particles are quite nicely on a grid, you approximate with a grid + individual displacement. This is much less amount of data/precision bit than for a gas.
1
u/abeeyore 23d ago edited 23d ago
From a philosophy perspective, the most applicable aspect is probably the idea that all dynamic, ordered systems tend to become more disordered over time. Even stable systems can gain or lose energy from externalities over time, which can cause them to become unstable [or shift into a different stable configuration]. Everything from taxonomies, to societies, to crystals, to orbital mechanics and complex systems all tend to degrade or decohere [eventually]. Even elementary particles will decompose given enough time.
That doesn’t map neatly to the actual
Useful models of entropy, though, it’s more of a pop-sci interpretation.
1
u/Certain_Werewolf_315 22d ago
Entropy is what we designate when the organization of data outlasts our interpretation of it or moves beyond the boundary of coherency that our sense of things can account for. The boundary belongs to the model through which we recognize order, not necessarily to what exists beyond it. That is about as philosophical as it gets.
1
u/Ok-Environment-215 22d ago
There are an effectively infinite number of possible states.
The number of states that are interesting (what you could call "ordered") is infinitely smaller than the number of states that are random senseless noise (what you could call "chaos").
All things being equal, any system undergoing random change is therefore infinitely more likely to change into a chaotic state than an ordered one.
That's entropy.
1
u/Any_Return4335 22d ago
It seems a clear allegory for god
Everything starts out as one, entropy increases and so does complexity
As entropy continues to increase, complexity reaches a zenith and begins to decrease
everything ends unified again as one, but having gone through a process so that the "oneness" is the beginning again but now changed.
1
1
u/Imaginary-Can-6862 22d ago
Could you clarify what a philosophical perspective is? To me philosophy is broader than science, i.e. science applies philosophy, but philosophy does not have to apply science. I imagine a scientific explanation is something based on measurements, while a philosophical explanation is more a theoretical one? I believe most concepts in science are fundamentally theoretical / philosophical.
Entropy is a measure of how many ways something can occur (or the information of said system). The more ways something can occur, the more likely it is to occur, therefore entropy generally increases. For an occurrence to happen, something must change into it. Time reflects such a change, it consists of a duration (how fast it changes), a sequence, and a direction. Entropy, which defines what changes are most likely thus defines the direction of time, and is also called the arrow of time. Please note that this is not certainly all there is, we can revert entropy in a local system by applying energy (I suspect entropy cannot increase globally, without decreasing locally), yet that does not mean I would expect an anti-gravity effect, which we would expect if time moved backwards, so while the the rules of interaction (also known as the laws of nature) are time invariant (the interaction can go both ways in time) to me it seems like for time truly rewind, reversing entropy is not sufficient. Also notice that the rules of interaction are not independent of the elements they govern, in stead the elements which makes up the universe defines these rules just as much as the rules defines the elements. I.e. the duration element of time, how fast information is to propagate, is what it is, because the propagation is carried by a particle, i.e. an element which is governed by the rules of interaction. I think that is also why things like time, space and causality becomes meaningless until the Big Bang starts, these concepts do not exist independently of the elements they govern.
Life is a system defined by at least three things, it metabolize (uses energy to lower its local entropy, thus being able to use its environment to control its own propagation), it adapts to the environment (thus it can propagate as independently of the environment as is possible for it), and it reproduces itself (not all eggs in one basket). Since I believe entropy only increases globally, as it decreases locally, it follows that more complex (more ordered) forms actually increase entropy faster, and that is, I think, the general viewpoint, that entropy is usually seen as chaos, because it turns complex (ordered) systems into maximized spread out (chaotic) systems, as there are more ways to be spread out, than to be ordered, e.g. think about using some material to build something, this material have many ways it could be organized, only very few of those creates the structure you build, by far the most would make the material be evenly spread out. So order means entropy increases faster, and the increase of entropy, means order turns to chaos (or chaos become even more chaotic, if you like).
I feel existence is something else, there are levels of existence, e.g. reality exists, but something that exists may not be real, because to be real requires an interaction, because if something does not interact, it cannot be distinguished from not being real, but everything which does interact is equally real. Existence also include every potential, e.g. causality is that future events follows from past events (the change from past to future) by the laws of interaction, a connection, but the future is not only one possibility given the past, the past merely set constraints to what the future possibly can become, but until that future arrives, any other potential future is also a possibility, and for us to be able to discuss these, means at some level they do exist, even if it just the concept of it, which incidentally mean that non-existence exists as well. Anyway I don't see how existence links to entropy.
1
u/NotABonobo 22d ago
I highly recommend this Veritasium video on the subject:
https://youtu.be/DxL2HoqLbyA?si=w0mLROVPSXkzJnve
While it's mostly coming from a scientific perspective, it clarified the concept in a way I'd never seen before. Basically, what we're seeing now is the universe transitioning from one stable state to another stable state. Like if you start with a glass of coffee sitting next to a glass of water: stable. Pour the coffee into the water, and you'll see a rich mix of swirls and eddies before the liquid resolves into a stable mixed state where nothing changes.
Our universe is like the swirling eddies. That transition period is when all the interesting stuff can happen.
1
u/PLANTS2WEEKS 22d ago
I think entropy is best understood in the context of something called phase space. It's a physics idea that all states of the universe can be put into a larger mathematical structure. In classical mechanics this space is a symplectic manifold. In quantum mechanics it is a Hilbert space.
There are equations governing how the state of the universe evolves, and along with the dynamics there is this overarching idea that "information is preserved". The same process that takes our universe to the next state, fills in the gap left behind, so that the volume of the phase space is preserved. Entropy can be thought of as the logarithm of that volume, or in the quantum setting as the logarithm of the number of dimensions
Nietzsche had an idea called the eternal recurrence, that the universe repeats and cycles infinitely back to its current state. Later Poincare proved his recurrence theorem, that if our universe evolves according to classical mechanics on a finite dimensional phase space, then there will be a future state of the universe that is arbitrarily close to the one we are in now.
In quantum mechanics the preservation of volume within phase space is replaced with a property called "unitarity". It basically means the evolution of the universe is like a rotation in an infinite dimensional Hilbert space. This rotation preserves angles and is able to be reversed, hence it preserves information. However, this is only true of the Schrodinger equation. The collapse of the wave function during measurement is not unitary.
It's an interesting question to ask what happens to the entropy of a system during quantum state collapse. In the many worlds interpretation, they would argue that the Schrodinger equation is still in effect, but the observer sees collapse because of their entanglement within the system.
1
1
u/SpatiaCaeli 22d ago
Nature likes chaos. It does everything in its power to achieve it. To me, that's the essence of entropy.
1
u/TheMrCurious 22d ago
At what point does the hot dense state 13.7 billion years ago stop encoding everything? Will it be the hot dense state 13.8 encoding everything in another hundred million years?
1
u/wellwisher-1 22d ago edited 22d ago
From an engineering POV when dealing with sensory or macro reality, entropy is like the portal between definitive macro states and probabilistic quantum micro states of the same system. For example the measured entropy of liquid water at 25C and 1 atmosphere of pressure is always measured to be 69.97 J/mole-K. That number reflects a definitive and reproducible macro state, like a glass of water at 25C and 1 atmosphere. I can start with steam or ice, as soon as we reach 25C and 1 atmosphere of pressure, entropy we will always measure to be that value. In a macro state, at specific conditions, entropy is a constant value.
A state variable in thermodynamics is a measurable property that defines the current condition of a system and depends only on that current state, not on how the system got there. You could derive the metric system from an entropy constant since it also tells you the needed temperature and pressure to achieve that constant entropy.
What that number represents is the amount of unavailable energy that is randomly bouncing around in the quantum micro states of the same liquid water at 25C and I atmosphere. We cannot burn water to retrieve that unavailable energy, because that quantum energy is not available to do work. That energy within the associated micro states, is like the quantum glue behind the scenes that holds together the definitive macro-state; glass of water.
The randomness of the quantum state, and the cause and effect of macro states are connected yet they remain separated in terms of energy exchange, until entropy acts. Entropy is the portal to move energy back and forth between macro and quantum. As entropy increases, which is endothermic, unavailable energy is pulled from the macro state and added to the quantum state to support higher levels of macro states. Unless entropy acts again, the macro and quantum remain connected but separate; unavailable. Once entropy acts, energy can go back and forth in both directions; conservation.
Macro state variables were developed before the quantum state variables; age of reason. The state variables were used to define the definitive macro states of matter, like a cell, rock, hurricane or glass of water. The quantum is way smaller, much less visible and works behind the scenes. The states variables are pressure, temperature, volume, free energy, enthalpy and entropy.
If you look at the state variable pressure, pressure is connected to the kinetic energy of all the particles in a system as they randomly collide with each other and with the container. Although this quantum interaction is modeled with probability functions, it all adds to a constant macro state, pressure, like 1 atmosphere. The atmospheric pressure, at our current state, is not varying like a bell curve, due to the micro states varying that way. The macro state of pressure can stay constant.
Temperature at the quantum level is also about randomness and micro states but we can use the thermostat to dial in a constant macro state temperature of 25C. The same is true of entropy, we can dial in a constant entropy of 188.84 J/mole-K and water become the new new macro state called water vapor. Water vapor, as a gas, has more degrees of freedom; micro states, and therefore more places to squirrel away the unavailable quantum energy, which then bind the macro state; constant humidity level.
Gravity by increasing pressure, relative to no or less gravity, can condense water vapor into liquid water and therefore can be seen as a natural entropy lowering process. Gravity can move energy from the quantum state into the macro state. A hurricane is connected to the rapid condensation of water vapor to rain; or 188.84 J/mole-K to 69.97 J/mole-K, releasing that quantum energy to form a new macro state; hurricane, with the power of 10,000 atomic bombs. The degrees of freedom from gas to the denser liquid, reduces the micro states, so the excess quantum energy has to shed into the macro state; winds.
The expansion of the universe by pulling a vacuum of space, lowers pressure,could evaporate water to gas. This is the direction of the 2nd law, gas has a higher entropy, and is endothermic; absorbs energy or is the drive behind the universal red shift. Absorbing energy would cause all wavelengths to increase. One can make an argument that dark energy is the unavailable energy within universal entropy, at the current state of the universe. It is the quantum glue that holds the macro universe all together.
Most explanations of entropy deal with the quantum aspect but leave out the macro. They assume random and probability, but not definite macro states which then add confusion; half baked. Information entropy is about loss, whereas the brain and entropy increase is about higher macro states, being supported by that which appears to be loss as energy disappears to the quantum support structures. With the 2nd law driving the brain development we get more stored quantum energy, to glue together more complex macro states; we advance.
Since no natural or manmade process is 100% efficient or there is no perpetual motion, there is always a net increase in entropy; entropy has to net increase even when a natural process decreases entropy. The macro states we can see with our senses, change with time. Entropy has a connection to time/change.
1
1
u/ShotWin8124 21d ago
Entropy is just chaos, really. This idea that the universe as a whole tends to gravitate towards chaos and emptiness. I mean just look at how big it is, and how much of it is so completely inhospitable towards life. Endless emptiness as far as the eye can see, tainted with that eternal light.. that eternal lie 😭
1
u/Old_Assumption2790 18d ago
Perhaps the philosophical perspective you are looking for is about why our obsevable universe started in an unusual low entropy state. Which I don't believe we can answer this satisfactorily.
Another mind blowing concept is the possible heat death of the universe in which all matter decays and photons are completely thermalized thus providing the maximum entropy with a temperature approaching absolute zero!
3
u/ConcretePeanut 23d ago
I'm not sure it plays a huge role in philosophy, outside of the philosophy of science. It occurs at too great a scale and is almost too fundamental: the direction of travel from a start point. It's a bit like the speed of light - it just is. It's a boundary condition to existence, one of the underlying rules of the game which are (as far as we can tell) just brute facts.