A bit better than a kelvin

After thermometers were first built in the 17th century, empirical observations spawned theories around energy and temperature. In 1865, those observations led German physicist Rudolf Clausius to introduce the idea of entropy, which explains the inevitable dissipation of energy in thermodynamical processes as a kind of measure of irreversible transformation. Today, statistical mechanics defines entropy as a fundamental quantity measured in joules per kelvin, units that relate energy transfer directly to temperature.

Bédard et al. challenged the use of the Kelvin scale, arguing that the informational nature of entropy makes measuring temperature in joules per bit -- a unit that compares energy amount to data amount -- more appropriate.

“There is a circularity problem in statistical mechanics: entropy is defined first, but its units depend on a yet-to-be-defined temperature,” said author Charles Alexandre Bédard. “Assigning entropy its own unit resolves this and leads naturally to expressing temperature as joules per bit.”

After connecting the inconsistency around entropy to those historic macroscopic theories, the researchers honed in on the role of information in thermodynamics; the notion that entropy amounts to information capacity; and, finally, the idea that temperature bridges information capacity with energy.

“The concepts of entropy and temperature would be viewed quite differently today if computer science had been invented before thermodynamics, as entropy was initially an obscure concept,” said author Xavier Coiteux-Roy. “Today, we understand quite well that entropy is a form of information that can be counted in bits, and that thermodynamics is really about the relation between energy and information. Expressing temperature as joules per bit simply makes that relation explicit.”

Source: “Temperature as Joules per bit,” by Charles Alexandre Bédard, Sophie Berthelette, Xavier Coiteux-Roy, and Stefan Wolf, American Journal of Physics (2025). The article can be accessed at https://doi.org/10.1119/5.0198820 .