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Comment by photochemsyn | Hacker News Reader

Here's the apparent important source paper, Feb 2022 in Physical Review Letters:

https://journals.aps.org/prl/pdf/10.1103/PhysRevLett.128.080...

Figs 1 and 2 show the setup. Here's the conclusion:

> "This gives a clear proof of the compatibility of constructor-based irreversibility with unitary quantum theory, providing a frame for the emergence of thermodynamical irreversibility in quantum mechanics."

It seems like an extraordinary claim, but is very interesting. The theoretical framework (constructors) is a bit confusing. Hopefully this will be replicated.

I recall someone talking about something rather similar once, related to so-called chaos theory (now more generally called 'sensitive dependence on initial conditions'), which describes how deterministic systems can give rise mostly unpredictable phenomena (strange attractors etc.), in which indeterminate quantum states at the atomic level are the ultimate cause of the phenomenon.

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Chaos theory is orthogonal to quantum theory. Neither depends on the existence (or nonexistence) of the other.

Chaos is unpredictable but for a different reason than quantum systems: Chaotic systems are unpredictable because we can never measure the real world perfectly (even ignoring quantum weirdness) and that lack of precision in measurement coupled with nonlinearity means our measurement errors amplify quickly. Nevertheless, chaos is theoretically deterministic. It's just not practically deterministic (except in the coarse-grained statistical sense of saying "the system's position in phase space is somewhere on a strange attractor path bounded by X.")

Quantum systems are not even deterministic in theory, let alone practice. And ironically quantum systems are fundamentally linear. So the spookier theory in a sense is based on more tractable math.

> Quantum systems are not even deterministic in theory, let alone practice. And ironically quantum systems are fundamentally linear.

It's important to note that the parts of quantum mechanics that are linear are also fully deterministic - the Schrodinger equation predicts the evolution of the wave function of a system with exact precision (as do the more complex equations of QFT).

The part that introduces non-determinism is the non-linear adjustment of the Schrodinger equation that you have to perform after a measurement - the Born rule, also called wave-function collapse. Here the complex-valued wave function of a system randomly takes a single real value at the moment of measurement. It does go back to its deterministic linear evolution afterwards though, but you have to perform this non-linear adjustment.

This non-linear adjustment can be interpreted in many ways, but without it QM doesn't agree with even the most basic experiments, so one way or another it is a vital part of the theory, rendering it non-linear overall.

Well-said. I was a bit sloppy in my terminology because the math of quantum computing is mostly linear (albeit complex) but I was thinking of the Schrodinger part.

When qbits have to be read, we convert them from complex to real and that step is both nonlinear and nondeterministic.

Chaos is only deterministic with infinite precision. Since the universe isnt the kinds of place where position-momentum etc. have infinite precision, chaos isnt deterministic.

Chaotic orbits of whole moons are non-deterministic on quite short time horizons.

Since all these phenomena of chaos are inherent in the differential equations, how can they possibly have anything to do with quantum states? The sensitive dependence on initial conditions is a mathematical property of the description of the chaotic systems. It’s a closed mathematical system that makes no reference to any physical reality.

Here's the quote, it was in some talk he gave:

The chaos can act as a magnifier of quantum fluctuations so that they can produce sizable effects in the world around us. But we know that that can happen often. - Murray Gell-Mann

I guess the idea is that if you have a collection of particles in a system that displays sensitive initial dependence, then any quantum jiggling gets rapidly amplified.

[edit] As you note this doesn't explain the chaos phenomena, because a stable dynamic system would squelch any quantum weirdness rather than amplify it.

yes, chaos theory, including strange attractors, is still deterministic. it acts at a level where the tiny probabalistic effects of a multitude of tiny particles cancel out in ways to miraculously make the larger subjects of interest predictable.

it's the same phenomenon underlying the wisdom of crowds (and the pricing function in fair markets): each individual can be wildly incorrect in an observation, but averaging many (independent) observations together reveals stable insight.

The differential equations which give rise to physical chaotic systems operate on quantum states interacting with each other at the atomic level, so there has to be a link of some kind.

I don’t understand your comment. Differential equations don’t give rise to physical systems.

Some nonlinear DEs exhibit chaos. That’s a purely mathematical property. Whether any particular DE is a useful model of a particular physical system is a matter for the imagination, and either backed up or refuted by experiment.

> Differential equations don’t give rise to physical systems.

Sure, but differential equations describe physical systems, and there is a canonical way to derive a quantum differential equation from a classical one by quantifying the classical Lagrangian using the Path Integral formulation. Giving a fairly natural distinction between the types of equations

> Whether any particular DE is a useful model of a particular physical system is a matter for the imagination, and either backed up or refuted by experiment.

This doesn't make sense to me. The Navier-Stokes equations are known to describe the classical behavior of water and are experimentally confirmed to predict things like trajectory. Their effectiveness has nothing to do with my imagination. If I write x=x' for the position vector of atoms in a fluid that will completely fail to describe anything physical.

The NS equations are a good description of approximately Newtonian fluids like water within certain regimes (nonrelativistic velocities, larger than atomic scales, far above 0°K, etc.). “Imagination” was not the best choice of word on my part. I meant that DEs are mathematical objects; their connection to physical systems is made by the scientist, not inherent in themselves. Whether the scientist guessed right is determined by experiment. The first people to suggest that the NS equations were a good description of Newtonian fluids had a model for fluid behavior in their imaginations. We know it was a good model because of experiment. But even if the NS equations described nothing in nature, their solutions, chaotic and otherwise, would have whatever properties they have.

Note that there is no Largrangian for the NS equations, by the way.

Yes, the quantumness of a differential equation is not a property of the differential equation, but a statement about one possible taxonomy of differential equation. Then, whether quantum-type diff eq's have unique properties pertaining to chaos conditioned on our knowledge of them being labelled 'quantum' is an interesting mathematical question.

> Note that there is no Lagrangian for the NS equations, by the way.

I don't know much about fluid dynamics, but I was under the impression that Bennett derives the Lagrangian form in the book Lagrangian Fluid Dynamics

There is a clash of terminology: the Lagrangian formulation of fluid dynamics follows the path of fluid particles, in contrast to the Eulerian form, which observes the fluid passing by a fixed coordinate system. In general dissipative systems don’t have time-independent Lagrangians.

yep, that sounds right to me. also I see you're the author of the Noether article from Ars Technica. I enjoyed the read.

The article presumably being https://arstechnica.com/science/2015/05/the-female-mathemati...

I’m glad, thanks!

Good discussion, thanks!

It looks like in the results section eqs (8)-(13), they give the main thrust of their idea. To demonstrate that not all machines are reversible they have to take the limit of the number of qubits of their machine as n goes to infinity, so their result is still in the limit, same as the typical laws of thermodynamics.

So this is primarily an interesting mathematical restatement at the quantum level. I don't know how useful this is, not having much knowledge about existing quantum information theory/thermodynamics.

> sensitive dependence on initial conditions

isn't that the wolfram thing? Simple patterns create complex unpredictable patterns? And our universe are just made up a few very simple rules and in combination it created this complex universe. Yeah most ideas has being around for a long time, it is just now we have the technology to verify some of these claims.

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