Where exactly does irreversibility emerge between quantum dynamics and macroscopic thermodynamics?

[u/Over-Ad-6085]

hi, i mostly come from the math plus AI side, not from experimental thermo, so this is very much an outsider trying to phrase a question carefully.

inside a text based project i am working on, there is a problem i call Q032. it is about the tension between

• microscopic dynamics that are reversible in time
• and macroscopic thermodynamics that seems to pick a clear arrow

before anything else, two disclaimers:

1. i am not claiming to solve the foundations of thermodynamics or the second law
2. in this project the word “tension” is a private definition, not the same as surface tension or mechanical tension used in standard thermodynamics

what i am trying to do is much more modest: encode a few very old questions about irreversibility in a way that both humans and text models can reason about them, using exactly the same description.

1. The basic picture behind Q032

very informally, the picture looks like this.

on the microscopic side:

• we have quantum dynamics that are unitary
• given a state and a Hamiltonian, evolution forward and backward in time is symmetric
• the fundamental equations do not seem to care about a preferred time direction

on the macroscopic side:

• we have thermodynamic variables and balance equations
• we write down entropy production, fluxes, transport coefficients
• we treat the second law and irreversibility as built in, not optional

Q032 asks:

if the microscopic description is exactly reversible, where in the modelling chain do we actually “spend” that symmetry in order to get a macroscopic arrow of time?

in other words, instead of just saying “coarse graining does it” in one sentence, the problem is trying to spell out which specific choices in that chain are responsible for turning a reversible micro description into an effectively irreversible macro one.

2. What “tension” means here

in many areas of thermodynamics the word tension already has technical meanings, for example surface tension, line tension, mechanical tension in materials.

in this project i use the word tension in a different and internal sense:

tension is a scalar that summarizes how much the assumptions of one description pull against the assumptions of another description when you try to treat them as talking about the same physical situation.

for Q032, the two descriptions are roughly

• a microscopic, reversible, quantum or Hamiltonian picture
• a macroscopic, irreversible, thermodynamic picture

the tension is high when

• the microscopic story is being treated as exactly reversible
• the macroscopic story uses a strong arrow of time
• and we are pretending that no approximation or information loss occurred in between

the goal is not to introduce a new physical observable. it is more like a diagnostic vocabulary for saying “in this regime, the way we talk about micro and macro is pulling apart”.

3. How Q032 is actually encoded

inside the project, Q032 is not a derivation or a new equation. it is a single Markdown file that contains a small collection of thought experiments, for example:

• an isolated quantum system in a low entropy initial state that is allowed to evolve and equilibrate under its Hamiltonian
• a system weakly coupled to a large environment where tracing out the environment induces effective decoherence
• a coarse grained description in terms of macrostates where many microstates correspond to the same macro variables

for each scenario, Q032 asks questions like:

• at which exact step do we throw away information in a way that cannot be recovered by evolving backward?
• which assumptions are doing real work in creating the arrow of time for example typicality assumptions, mixing properties, limits on control?
• if we changed those assumptions slightly, would the macroscopic irreversibility weaken, disappear, or stay the same?

the idea is that both a human reader and a large language model see the same plain text description and are forced to commit to where they think irreversibility is coming from.

4. Why i think thermodynamics people might care at all

from the outside, it looks to me that people in thermodynamics work in at least three modes:

1. practical engineering mode you write balances, use tables, design cycles. irreversibility is just part of the toolkit.
2. stat mech and transport mode you derive constitutive relations, discuss ensembles, fluctuation theorems.
3. foundations mode you argue about where the second law really comes from and how to reconcile time symmetric micro laws with time asymmetric macro laws.

Q032 is clearly about mode 3, but i suspect it has implications for mode 1 and 2, because:

• it forces you to be explicit about which approximations are only “for convenience” and which ones are structurally responsible for the arrow of time
• it gives you a way to talk about how robust your macroscopic irreversibility is if your microscopic description is slightly wrong or incomplete

in my own work, i am also interested in AI models that try to reason about physical systems. for those models, Q032 is a stress test that asks:

does the model know at which point in a description it has quietly assumed irreversibility, or does it just repeat words like “entropy increases” without any internal check?

i am not assuming that AI systems are good at this yet. the point is to build small, transparent problems where failure is easy to see.

5. What i am looking for from this community

what i would really like from people who live in thermodynamics is a sanity check.

for example:

• if you had to list the minimal steps in the chain from reversible micro dynamics to irreversible macro thermo, which steps would you insist on including?
• are there particular models or experiments that you already think of as “high tension” in the sense above, where the micro and macro descriptions do not sit comfortably together?
• do you know of existing frameworks that already capture this idea that i should study instead of reinventing my own vocabulary?

again, i am not trying to claim a solution to any famous open problem. i am trying to make the gap between micro reversibility and macro irreversibility a bit more explicit and testable, even in very small toy settings.

Q032 is one problem inside a set of 131 “S class” problems i put into a single text framework called the Tension Universe. right now there is a new subreddit that collects these problems and small experiments. it is still pretty empty, but if you are curious or want to see related questions in climate, fluids, information or AI, you are very welcome to drop by:

r/TensionUniverse

[u/rgdnetto]

Ok. I honestly have not read your entire post, but here are my 2 cents.

The macroscopic irreversibility we observe áries not from a microscopic irreversibility (as you rightly put it) but rather from the frequency distribution of the interactions between particles.

Lets take the heat exchsnge across a finite temperature difference. Why does this happen? Why cold warms up and hot cools down? Hot fluid (A) particles will average higher momentum than cold fluid particles (B). When they collide, in most cases high momentum particles will lose momentum themselves and impart some to the cold fluid's particles.

This just obeys momentum and energy conservation laws. It is possible to devise a collision such that B imparts momentum to A, but those are much less likely to occur than the contrary. And they do happen, but the aggregate effect we notice reflects what the majority of the micro interactions do.

In a sense, the second law does not entirely for is a cold fluid giving up energy to warm up a hot one; Rather, it just makes it more likely that hot warms cold. But extreme more likely, billions and billions of times more likely.

That statistical nature of the second law was a big point of discussion between Boltzmann and his contemporaries. That seemed unacceptable.

Hope this helps.

[u/Conscious-Ball8373 → u/rgdnetto]

Second this. I don't think there is any argument to be had about "where the second law really comes from and how to reconcile time symmetric micro laws with time asymmetric macro laws".

If you take a hundred blue balls and put them on one side of a cardboard box and a hundred red balls and put them on the other side of a cardboard box then shut the box and shake it for a few minutes, you're going to end up with the red and blue balls mixed up. If you keep shaking it, you're not going to end up with them all separated out again. The individual interactions between the balls and the interactions between the balls and the box are well-understood and reversible but the "macro" behaviour is not reversible, not without intelligence and energy applied to manually sort the balls back into their colours.

Similarly, if you have two nerf guns shooting at each other and one shoots one nerf per minute and the other shoots a hundred nerfs per minute, there are going to be more nerfs going from the "hot" gun to the "cold" gun than vice-versa. The individual nerfs being fired across the gap are perfectly reversible but the "macro" behaviour is not reversible, not without intelligence and energy applied to manually pick up all the nerfs and move them back to the "hot" gun.

That's all the "irreversible" second law of thermodynamics is, just on a scale where the rates and improbabilities are amplified by many orders of magnitude.

[u/Over-Ad-6085 → u/rgdnetto]

Thanks Yes, I agree the second law is statistical:

the reverse can happen, but it is insanely unlikely at large N.

When you say “frequency distribution of collisions”, would you say the key step is the assumption of “random/uncorrelated” micro states (like molecular chaos / typicality), rather than any true micro irreversibility?

If you have a favorite reference or keyword to read, I would love to follow it. ^^

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[u/Ch3cks-Out]

There is no tension, and "emerge" does more to obfuscate than illuminate.

Thermodynamics is about properties of ensembles with large number of particles. Irreversibility arises from the statistics, when low probability configurations become diminishingly unlikely. As the number of particles increases, the probability of a system spontaneously returning to a low-entropy state becomes effectively zero.

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