Every so often a paper arrives promising that one tidy equation explains atoms, evolution, snowflakes, and the fundamental nature of existence. The correct response is not to sneer. It is to lean in, enjoy the show, and keep one eye on where the coins go.
The paper is Melvin Vopson's "The second law of infodynamics and its implications for the simulated universe hypothesis," and it has been quietly reappearing in feeds for three years because of that last clause. It is the "we might be living in a simulation" paper. I want to walk you through what it actually says, because the real thing is more interesting than the headline, and the places where it breaks are more instructive than the places where it holds.
You do not need the math. You need one idea and a healthy skepticism, and I will supply both.
Start with the law everyone already half-remembers. The second law of thermodynamics says that in a closed system, entropy tends to increase. Entropy is disorder, or more precisely, the number of ways the pieces of a system can be arranged without you noticing a difference. Drop an ice cube in coffee and the tidy arrangement (cold here, hot there) dissolves into a uniform lukewarm mess. The mess has more possible arrangements than the order did. That is the arrow of time. Things spread out. Your desk does not spontaneously tidy itself.
Now the twist. Vopson draws a distinction between two kinds of entropy living in the same system. There is physical entropy, the thermodynamic kind above. And there is information entropy, which measures the uncertainty in the actual pattern stored in the system. The bits, not the heat.
If you have ever run a zip utility, you already have the intuition he is reaching for. Compression finds the most efficient way to store a pattern, throwing away redundancy until nothing is left to squeeze. Vopson's suggestion is that the universe does this on its own, everywhere, as a matter of physical law. And a universe that automatically compresses its own data looks suspiciously like a program written by someone who was worried about running out of memory.
That is the whole pitch. Everything else in the paper is Vopson pointing at different corners of nature and saying: look, compression here too.
He offers four demonstrations. They are worth taking one at a time, because they do not all fail in the same way, and a couple of them do something genuinely clever before they overreach.
Write the word INFORMATION onto a magnetic medium, simulate it sitting there, and the bits slowly scramble until the message erases itself and the information entropy hits zero. Data rots. Anyone who has opened a twenty-year-old hard drive believes this instantly.
The catchThis is just thermodynamics wearing a new hat. The bits scramble because heat randomizes the little magnets, which is the ordinary second law doing ordinary work. Calling the decay a new information law is like discovering that ice melts and naming it the first law of puddle dynamics.
He tracks the information content of SARS-CoV-2 variants over the pandemic and reports it falling as mutations accumulate. From this he floats a large idea: mutations are not truly random, they are steered toward lower information. Darwin, gently corrected.
The catchTwo problems, and the second is the one to remember. First, random mutation should raise information entropy, not lower it, so the result begs for an explanation the paper never supplies. Second, Vopson writes in his own methods that the data points were "carefully selected to emphasize the linear trend." He is telling you he chose the dots that made the line straight. In clinical terms, he unblinded himself and kept the responders.
This is the strongest section. There is a well-known rule in chemistry (Hund's rule) for how electrons arrange themselves in an atom, and it has always been justified by fiddly energy arguments. Vopson shows that the arrangement chemistry actually observes is also the one with the lowest information content. The two criteria agree, cleanly, across every orbital he checks.
The catchAgreement is not causation. He has found that his information quantity is minimized exactly where the energy is minimized, which is elegant and might even be telling us something. But energy minimization already explains the rule. Showing that a second bookkeeping method lands on the same answer does not prove the second method is the cause. Two clocks that agree do not mean one is driving the other.
A symmetric shape carries less information than a lopsided one, because you can describe it with fewer independent facts. A square is just a side length and "repeat." Vopson computes this for triangles and quadrilaterals and finds, reliably, that more symmetry means less information. Nature loves symmetry; nature, therefore, loves compression.
The catchThe measurement is rigged by the setup. He defines information using the number of distinct sides and angles, so of course the shape with more repeated parts scores lower. He has built a ruler that reads "symmetric" as "small" and then expressed surprise that symmetric things come out small. The snowflakes are lovely. The argument is circular.
The fifth corner is the universe itself, and here the paper makes its one genuinely thoughtful argument before spending it recklessly.
The setup is a real puzzle. Our universe is expanding, and as it expands its physical entropy keeps rising. But run the clock backward and the early universe, tiny and smooth and nearly uniform, looks like it was already near maximum entropy for its size. So where is all the new entropy coming from as space grows? Vopson calls this the entropic paradox, and his proposed fix is to add a hidden information term to the books that balances the ledger. It is a serious-sounding idea and not a stupid one.
Then comes the leap. Because the information term has to shrink over time to keep the accounts balanced, and because shrinking information looks like compression, and because compression looks like something a programmer would build to save memory, Vopson concludes that the universe is probably a simulation. Each step is a plausible-sounding nudge. Stacked together, they carry you from a bookkeeping question in cosmology to Elon Musk's favorite dinner-party theory, and no single step is where you can plant your feet and object. That is precisely what makes it a magic trick rather than a proof.
The popular press covered this uncritically, which is the popular press doing its job. The physics community was quieter and less kind.
Sabine Hossenfelder, reviewing the broader infodynamics program, concluded that it makes no sense and should not have been published, on the grounds that it misuses the concept of information and contradicts settled results on entropy. Vopson's rebuttal fairly notes that she offered no line-by-line mathematical counterexample, which is a point about debating manners, not about whether he is right.
The more useful critique comes from Harrison Crecraft, writing in Entropy, who takes the idea seriously enough to try to repair it and in the process names the load-bearing flaw. Information entropy, he points out, depends on what the observer already knows. It is not a fixed physical property of the system sitting out there in the world. Change your assumptions about the starting probabilities and the number changes. You cannot build a fundamental law of physics on a quantity that shifts depending on who is looking and what they assumed before they looked. The whole edifice rests on treating a bookkeeping choice as if it were a measurable feature of nature.
One more thing worth knowing. A fair amount of the supportive literature comes from journals and an institute in Vopson's own orbit, funded in part by the crowdfunding backers he thanks by name in the acknowledgments. That does not make the work wrong. It does mean the applause you find is not the same thing as independent replication, and the two are easy to confuse from the outside.
The second law of infodynamics is a beautiful piece of pattern-matching wearing the costume of a physical law. The individual observations range from "true but already known" to "true because I defined it that way," and the simulation conclusion is a rope bridge built entirely out of the word "resembles."
Read it. Enjoy it. It is a wonderful example of how a smart person can be led somewhere ridiculous by a sequence of reasonable-sounding steps, which is a more valuable thing to watch than a paper that simply gets everything right.
Sources
The paper: Vopson MM. The second law of infodynamics and its implications for the simulated universe hypothesis. AIP Advances 2023;13(10):105308. pubs.aip.org
The substantive critique: Crecraft H. The Second Law of Infodynamics: A Thermocontextual Reformulation. Entropy 2024;27(1):22. PMC11765112
The public critique and the reply: Hossenfelder's video commentary, and Vopson's formal response in IPI Letters. ipipublishing.org