Run a current through a wire, and the wire heats up. Anyone who has ever touched a phone charger knows this. Physicists call this heating Joule heating, after James Joule, who in the mid-19th century measured how much heat electricity produces. Since then, the formula has been simple: the greater the resistance and the current, the hotter the wire.
But what happens at the very bottom of this picture — at the level of individual electrons and atoms? There, everything obeys quantum mechanics, which works differently. In the quantum world, there is no friction in the usual sense. A particle can pass through obstacles without touching them, and energy is transferred only in discrete chunks. The authors of the new study took a simple model of a quantum wire and tried to understand where heating comes from in it. And they ran into a surprise: if you track each electron honestly, according to the laws of quantum physics, entropy, the measure of disorder, does not increase at all. The wire stays cold.
So where does the heat in a real wire come from? The authors' answer: measurements create it. To make the wire heat up, you need to place tiny sensors along it — thermocouples that continuously take readings. Each such sensor obtains information about the state of the electrons and thereby interferes with their lives. This interference is what generates irreversibility. The information obtained by the sensor turns into heat, just as erasing a record on a hard drive releases a little energy. In a real wire, the role of such sensors is played by random collisions of electrons with lattice atoms. Each collision is a tiny measurement that pins down where the electron is.
The result is a beautiful picture: Joule heat is not just friction, but a payment for information. The wire heats up because nature constantly "observes" the electrons, forcing them to choose a definite position. The more such observations, the more heat. In the limit, when there are many sensors, the quantum wire heats up exactly as the classical Joule formula predicts. Quantum mechanics does not cancel the second law of thermodynamics; it hides its mechanism in the very process of measurement.
as written by the authors arXiv:2601.05514
As remarked by Boltzmann, the Second Law of Thermodynamics is notable for the fact that it is readily proved using elementary statistical arguments, but becomes harder and harder to verify the more precise the microscopic description of a system. In this article, we investigate one particular realization of the 2nd Law, namely Joule heating in a wire under electrical bias. We analyze the production of entropy in an exactly solvable model of a quantum wire wherein the conserved flow of entropy under unitary quantum evolution is taken into account using an exact formula for the entropy current of a system of independent quantum particles. In this exact microscopic description of the quantum dynamics, the entropy production due to Joule heating does not arise automatically. Instead, we show that the expected entropy production is realized in the limit of a large number of local measurements by a series of floating thermoelectric probes along the length of the wire, which inject entropy into the system as a result of the information obtained via their continuous measurements of the system. The decoherence resulting from inelastic processes introduced by the local measurements is essential to the phenomenon of entropy production due to Joule heating, and would be expected to arise due to inelastic scattering in real systems of interacting particles.
James Joule, after whom the heating of a conductor is named, was a brewer. He conducted his experiments on heat generation in his spare time, using brewery equipment.
In Stanisław Lem's novel Solaris, the ocean-planet reacts to human observations — similar to how in the quantum world, the very act of measurement changes the behavior of the system.