Thermodynamics is the science of how energy moves and changes form. It traditionally studies large, uncorrelated systems, like steam engines or refrigerators.
Quantum Thermodynamics Reveals New Limits for Microscopic Engine Efficiency
Scientists recently developed an exact formula for the efficiency of quantum engines. These tiny machines operate on principles differing from standard thermodynamics. This research helps us understand how microscopic systems behave when they are strongly coupled to their environments.
What Standard Thermodynamics Tells Us
Thermodynamics is the science of how energy moves and changes form. It traditionally studies large, uncorrelated systems, like steam engines or refrigerators. One key rule is the Carnot limit. The Carnot limit establishes the highest efficiency a heat engine can achieve when it utilizes two thermal reservoirs at varying temperatures. It says no engine can be more efficient than ηC = 1 − Tc/Th, where Tc and Th are cold and hot reservoir temperatures.
This rule, on the other hand, operates well for machines of a scale that is typical of everyday use since it implies that the system and its surroundings do not interact strongly with one another or share correlations.
The Role of Correlations in Microscopic Systems
The behavior of matter is different when it is on a very small scale. There is a common occurrence of quantum systems becoming substantially entangled with their surroundings. This process breaks down traditional assumptions about independence and renders standard thermodynamics insufficient for predicting machine performance.
The latest study calls these assumptions into question by accounting for every potential quantum correlation. The results reveal that microscopic quantum engines operate in two essential ways: the conventional thermal mode, which converts heat into work, and a recently discovered thermal mode.
Athermal Regime: Work from Correlations
The athermal ecosystem utilizes correlations as an entropic resource. These machines extract work not only from heat but also from the information contained in the system and bath’s entanglement. Surprisingly, engines that operate in this manner are capable of surpassing the efficiency of the traditional Carnot!
Because of this discovery, long-held beliefs on the limits of energy conversion on tiny sizes are called into question.
The Generalized Laws of Quantum Thermodynamics
The researchers developed new formulations of the first and second laws of thermodynamics. They intended these modifications for quantum systems that are periodically driven and coupled to multiple reservoirs. They incorporated interactions that might not preserve energy on average, which is a scenario that frequently occurs in devices of a smaller scale.
An Exact Energy Balance Equation
In order to determine the exact relationship between the overall amount of work performed throughout a cycle and the heat flows across all reservoirs, as well as changes in internal energies, including interaction energies, the team used the following equation:
Total Work = Sum of Heat Absorbed by Reservoirs + Change in System Energy + Interaction Energy Changes.
This generalized first law removes previous limitations seen in weak-coupling approximations commonly used before.
A More Complete Entropy Balance Formula
An updated version of the second law now takes into account all of the different correlation measures that exist between subsystems and baths, in addition to the changes in relative entropy that are from thermal reference states. As a result, an entropy equilibrium is achieved, which includes the creation of entropy that is not in equilibrium and is linked to irreversibility, in addition to extra contributions from initial correlations:
Total Entropy Change = Entropy Production + Changes in Mutual Information and Correlations Between System and Baths.
This new relation captures irreversible processes beyond classical thermodynamic descriptions, especially relevant at microscopic scales.
Additionally, to stay updated with the latest developments in STEM research, visit ENTECH Online. Basically, this is our digital magazine for science, technology, engineering, and mathematics. Further, at ENTECH Online, you’ll find a wealth of information.
Reference
- Aguilar, M., & Lutz, E. (2025). Correlated quantum machines beyond the standard second law. Science Advances, 11(41), eadw8462. https://doi.org/10.1126/sciadv.adw8462
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