November 27, 2025 by Ingrid Fadelli, Phys.org
Collected at: https://phys.org/news/2025-11-physicist-delineates-limits-precision-quantum.html
Quantum thermal machines are devices that leverage quantum mechanical effects to convert energy into useful work or cooling, similarly to traditional heat engines or refrigerators. Thermodynamics theory suggests that increasing the reliability with which all thermal machines produce the same thermodynamic processes in time comes at a cost, such as the wasted heat or the need for extra energy.
Drawing from theories and concepts rooted in thermodynamics, physicist Yoshihiko Hasegawa at the University of Tokyo recently set out to pinpoint the limits that would constrain the precision of finite-dimensional quantum thermal machines. In a recent paper, published in Physical Review Letters, he delineates these limits and shows that quantum coherence could reduce fluctuations, improving the accuracy of quantum thermal machines.
“Thermodynamic uncertainty relations have clarified an important ‘no free lunch’ principle: if you want an operation to be more precise, you must pay more thermodynamic cost, i.e., entropy production,” Hasegawa told Phys.org. “However, those thermodynamic uncertainty relations do not forbid, in principle, pushing entropy production arbitrarily high.
“If you could do that, the thermodynamic uncertainty relation would allow arbitrarily high precision. Yet for realistic quantum devices, it is clear that you cannot generate infinite entropy production. This means that, even before you specify any dynamics, the structure of the system must impose some ultimate precision limits.”
New bounds that are influenced by quantum coherence
In his paper, Hasegawa starts by considering a very general open quantum system (i.e., a system that interacts with something in its surrounding environment). Both this system and the environment only have a limited number of possible quantum states (i.e., they are finite-dimensional), and they evolve together following the rules of quantum mechanics.
“Using a framework known as information-theoretic inequality, and tools from quantum cooling/third-law literature, I derived lower bounds on the smallest eigenvalue that the environment’s state can have after any such dynamics,” said Hasegawa. “Combining this with spectral properties of Gibbs states gives dynamics-independent bounds.”
Essentially, Hasegawa derived new mathematical bounds that delineate how precise the output of quantum thermal machines can be. Notably, these bounds should not vary in accordance with the operation of individual machines over time.
“To assess the role of coherence, I compared the case of a thermal environment with a coherent Gibbs state whose populations are thermal but with added off-diagonal terms,” said the author.llustration of a quantum battery. Credit: Yoshihiko Hasegawa
Informing the future development of quantum thermal machines
As part of his study, Hasegawa also examined the case of a quantum battery and delineated bounds restricting its precision in storing energy. He also explored the extent to which quantum coherence would alter the fundamental limits that he derived.
“By bounding how these coherent corrections shift the smallest eigenvalue, one can show that coherence can tighten the precision bounds,” said Hasegawa. “Conceptually, the key contribution is to move from ‘cost-precision’ trade-offs that depend on particular dynamics (via entropy production to universal bounds that hold for any possible dynamics consistent with the initial setup). In that sense, the paper identifies fundamental limits on how precise a finite-dimensional quantum thermal machine can be, regardless of how cleverly it is driven.”
This recent work introduces new limits on the precision of quantum thermal machines, including quantum batteries, which could guide these systems’ future development. In the case of quantum batteries, Hasegawa showed that there is a clear trade-off, as one cannot simultaneously store large amounts of energy and obtain an arbitrarily high charging precision.
“The bound was derived under a very general quantum setup,” added Hasegawa. “Therefore, it can be applied to very general quantum systems. For example, it can be used for studying the ultimate accuracy limit in quantum machine learning.”
More information: Yoshihiko Hasegawa, Fundamental Precision Limits in Finite-Dimensional Quantum Thermal Machines, Physical Review Letters (2025). DOI: 10.1103/qh8p-4bxs. On arXiv: DOI: 10.48550/arxiv.2412.07271
Journal information: Physical Review Letters , arXiv
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