Two physicists at the University of Stuttgart have demonstrated that the Carnot principle, a foundational rule of thermodynamics, does not fully apply at the atomic scale when particles are physically linked (so-called correlated objects). Their findings suggest that this long-standing limit on efficiency breaks down for tiny systems governed by quantum effects. The work could help accelerate progress toward extremely small and energy-efficient quantum motors. The team published its mathematical proof in the journal Science Advances.

Traditional heat engines, such as internal combustion engines and steam turbines, operate by turning thermal energy into mechanical motion, or simply converting heat into movement. Over the past several years, advances in quantum mechanics have allowed researchers to shrink heat engines to microscopic dimensions.

"Tiny motors, no larger than a single atom, could become a reality in the future," says Professor Eric Lutz of the Institute for Theoretical Physics I at the University of Stuttgart. "It is now also evident that these engines can achieve a higher maximum efficiency than larger heat engines."

Professor Lutz and Dr. Milton Aguilar, a postdoctoral researcher at the same institute, describe the physics behind this surprising result in their Science Advances paper. In a three-question interview, they outline what they discovered and why it matters.

Rethinking a 200-Year-Old Efficiency Limit

Nearly two centuries ago, French physicist Sadi Carnot established the theoretical maximum efficiency that any heat engine can achieve. The Carnot principle, which later became part of the second law of thermodynamics, was formulated for large-scale systems such as steam turbines.

The Stuttgart researchers have now shown that this principle must be expanded when applied to systems at the atomic scale. This is especially true for strongly correlated molecular motors, where particles are closely connected in ways not accounted for in classical thermodynamics.

The Hidden Role of Quantum Correlations

Carnot’s original work showed that efficiency depends on temperature differences, with larger gaps between hot and cold leading to greater potential efficiency. What the classic formulation does not include is the effect of quantum correlations. These are subtle connections that arise between particles when systems become extremely small.

For the first time, the researchers derived generalized thermodynamic laws that fully incorporate these correlations. Their results reveal that atomic-scale thermal machines can convert not only heat into work but also quantum correlations themselves. Because of this added contribution, such machines can generate more work than classical theory allows, meaning the efficiency of a quantum engine can exceed the traditional Carnot limit.

What This Means for Future Technology

Beyond refining fundamental physics, the research opens new possibilities for future applications. A deeper understanding of how physical laws operate at the atomic level could speed the development of next-generation technologies, including ultra-small and highly efficient quantum motors capable of precise nanoscale tasks.

Such motors could one day power medical nanobots or guide machines that manipulate materials atom by atom. The range of potential uses is vast, highlighting how reexamining basic scientific principles can lead to entirely new technological horizons.