The new approach accurately predicts when systems like lasers may have negative absolute temperatures. Credit: Wladimir Bulgar/SPL/Getty
Researchers have proposed a new way to define entropy for isolated nanoscale systems1, making it easier to predict how temperature and energy are related in systems made up of just a few atoms, molecules, or electrons.
Instead of using an absolute energy range, the new approach looks at a smaller, relative energy window where the system's energy is likely to reside, says Ananth Govind Rajan at the Indian Institute of Science in Bengaluru. An isolated nanoscale system is one that doesn’t exchange matter or energy with its surroundings.
This new definition also accurately predicts when these systems will have negative absolute temperatures — situations where temperatures drop below zero on the Kelvin scale. This unusual behaviour occurs in systems like lasers and nuclear spin arrangements, where higher energy states are more populated than lower ones, unlike what is typically seen with temperature changes. Traditional entropy models, like Gibbs’ volume entropy, couldn’t explain these negative temperatures, leading to mismatches with experiments. Although Boltzmann's model predicted these temperatures, it did so even when they weren’t physically possible.
The new definition, drawing from quantum mechanics principles like the Heisenberg uncertainty principle and eigenstate thermalization, merges the strengths of both Gibbs and Boltzmann models. It gives a more accurate understanding of how nanoscale systems work and could be useful in areas where precise control of energy states is needed.
