A new study by Cnr Nano researcher Michele Campisi establishes a unified theoretical framework to describe ergotropy — the maximum usable energy that can be extracted from a physical system — across both classical and quantum physics.

The work, titled ‘Unified theory of classical and quantum ergotropy’, connects concepts that had long evolved separately in different scientific communities, from quantum thermodynamics on the one hand and classical fluids on the other, including plasma physics and astrophysics. The resulting theory applies across vastly different scales, from individual quantum systems to fluids and even galactic structures.

“Scientists working in different fields were essentially asking the same question — how much energy can be extracted from a system — but often without being aware of each other’s results”, explains Campisi. “In this work we unified these apparently distant approaches into a coherent and general picture”.

Ergotropy quantifies the maximum amount of energy that can be extracted from a thermally isolated system. While the concept plays a central role in modern quantum thermodynamics, analogous problems have long been studied in classical physics, for example in collisionless plasmas and astrophysical systems. The new study demonstrates that the classical and quantum formulations can be derived within a single analytical framework.

Beyond its theoretical relevance, the work addresses a question with broad practical implications. Energy extraction is central to modern technological society, from batteries and nanoscale devices to large-scale energy systems. “How much energy can be extracted from a single atom, from a material, or from a turbulent fluid such as the atmosphere or even a galaxy?”, says Campisi. “These questions can all be addressed within the unified theory of ergotropy presented in this work”.

The theory not only determines how much energy can, in principle, be extracted, but also identifies the transformations required to achieve optimal extraction. Possible applications range from fusion plasmas to quantum batteries, while future developments may extend to many other areas where energy management and conversion are crucial.

One of the most original aspects of the research is its strongly interdisciplinary character. By building a bridge between scientific areas that had remained largely disconnected, the work enables methods and ideas to move across the classical–quantum boundary, potentially opening new directions in both fundamental and applied research.

The study also revisits the relationship between classical and quantum contributions to ergotropy, showing that features associated with quantum coherence may persist in the classical regime, indicating that coherence does not necessarily constitute a uniquely quantum signature.

Interestingly, the origins of the work emerged directly from Campisi’s teaching activities. “While preparing lectures for my Quantum Thermodynamics course at the University of Pisa, I realized that related problems had already been investigated decades earlier in plasma physics and astrophysics, which eventually led me to connect these different theoretical approaches into a unified framework”, says the researcher.

The paper has been featured as an Editor’s Choice by EPL, recognizing work considered particularly significant and of broad interest by the journal’s editors.

Reference article: M. Campisi, Unified theory of classical and quantum ergotropy,  EPL 154 50002. DOI: https://iopscience.iop.org/article/10.1209/0295-5075/ae652c

[IMAGE: Futuristic science-fiction image, from magnific.com]