How to Measure Chaos in a System Without Knowing Its Rules ✎ express

Original: "A method for calculating entropy production without knowing transition rates or dwell times"
· John W. Biddle
arXiv:2605.27635 · 2026-05-26 · arXiv non-exclusive · independent analysis · 2 min
A scientist has found a way to calculate the rate of disorder growth by merely observing the system's changes in state.

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A busy intersection without traffic lights. Cars drive, brake, and change lanes, and from the outside, it looks like complete chaos. But if you watch for a while, you can notice a rhythm: the flow thickens and thins. In physics, this rhythm of disorder is called entropy: it shows how far a system is from calm equilibrium, like water in a boiling kettle.

Until now, measuring the rate of entropy increase required knowing all the rules of motion, like having a detailed map of the intersection with each driver's habits. But in a living cell or a turbulent flow, these rules are too complex or simply unknown. The author of the new work proposes doing without the map: you only need to record the state the system is in (for example, "many cars, congested" or "few cars, free-flowing") and how long the observation lasted. The moments of switching and their causes don't matter — the method works like a patient observer on a balcony who counts not individual maneuvers but the overall picture.

Entropy always increases: that's a law. But each system has its own growth rate, and that rate tells you how far the system is from equilibrium. For example, a healthy cell has one rate, while a diseased cell has another.

The secret of the method is that it relies on a simple idea: if a system frequently flits between the same states, entropy grows quickly; if it lingers for a long time, it grows slowly. You don't need to know why it transitions from one state to another — only the sequence of those states. It's like counting calories in a dish without a recipe: you don't know the ingredients, but you see how the plate's weight changes.

This approach is especially valuable for biology and nanotechnology, where tiny motors like the protein kinesin step along intracellular tracks. Now you can estimate their efficiency simply by tracking the motor's position, rather than taking it apart screw by screw. Or, say, understand how wasteful a cancer cell is compared to a healthy one, just from the chronicle of its states.

That same intersection from the first example can now be studied without knowing the traffic rules. Just watch from the window and time it, and you'll learn how far that flow is from a quiet night street.

The rate of entropy increase in living organisms is astonishingly low: if a person used energy as efficiently as a light bulb, a single sandwich would last them a whole day.

Scientists
Ludwig BoltzmannRudolf ClausiusClaude ShannonJacob BekensteinStephen HawkingWilhelm Wien
Concepts
entropy enthalpy Markov chain energy consumption principle of maximum entropy second law of thermodynamics ensemble average damping rate energy distribution Boltzmann equation mass production Michaelis-Menten equation thermalization Fermi's golden rule equilibrium non equilibrium power consumption mass flow rate information processing real time