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A study in Â鶹ÒùÔºical Review Letters (PRL) details a "Gambling Carnot Engine" that researchers report can attain 100% efficiency while also improving power generation.

The researchers present a feedback-controlled heat engine that strategically exploits thermal fluctuations at the microscopic scale, opening new pathways for energy harvesting in nanoscale devices.

The research, led by Dr. Édgar Roldán from the Abdus Salam International Center for Theoretical Â鶹ÒùÔºics, challenges two centuries of thermodynamic understanding by proposing a method to surpass what was once considered an inviolable limit in physics: the Carnot efficiency bound.

"I have always been fascinated by how engines work, from the engine of a car, or more sophisticated machines, both artificial, such as solar cells, or natural, such as cells and organisms," Roldán told Â鶹ÒùÔº, reflecting on his motivation for the research.

Strategic gambling

Standard heat engines, including the well-established Carnot engine, are bounded by the Carnot efficiency maximum: η = 1 – (T_c/T_h), where T_c and T_h indicate the temperatures of the cold and hot thermal reservoirs, respectively.

This bound, established by Sadi Carnot in 1824, has been considered absolute for two centuries. Exceeding this limit within classical thermodynamics would require violating the second law of thermodynamics itself.

The gambling Carnot engine (GCE) incorporates a gambling strategy derived from game theory and implemented in thermodynamics. The system utilizes an external controller or "demon," derived from Maxwell's celebrated thought experiment, to implement strategic measures according to specific criteria.

"The term 'gambling' was coined in a previous work by some of us, ',' published in PRL in 2021," Roldán explained.

"An analogy with gambling can be drawn, thinking, for example, in blackjack, where players may play in a round or not depending on the cards in their hand, and also following a specific criterion."

The innovation centers on the engine's isothermal compression phase.

During this step, the particle would normally undergo gradual compression as the trap stiffness increases slowly, a process requiring substantial work input.

However, the demon continuously monitors the particle's position using high-speed laser interferometry throughout this compression period.

When the particle crosses the trap center (position x = 0) before a predetermined deadline, the system immediately jumps to the final compression state at zero work cost.

The mechanics of microscopic efficiency

The engine operates using a colloidal particle—a microscopic polystyrene sphere suspended in water and trapped by focused laser beams. Unlike macroscopic engines with pistons and cylinders, this nanoscale system adjusts the particle's confining potential to produce thermodynamic cycles.

"The idea behind the GCE is to combine the key mechanism of energy extraction in a heat engine (converting part of the heat from a hot bath into extracted work, like in a car's engine) and that of an information machine (applying feedback at specific moments, like in a Maxwell's demon)," Roldán said.

The strategic advantage emerges from exploiting Brownian motion that causes the particle to jiggle around the trap center.

The particle typically fluctuates within a few hundred nanometers of the equilibrium position due to thermal energy from molecular collisions in the surrounding water.

The researchers determined that this gambling strategy produces a survival probability that falls exponentially with cycle time, meaning efficiency rises as operational timescales grow. In the quasistatic limit, efficiency approaches 100%.

Redefining efficiency within fundamental limits

The claim of surpassing Carnot efficiency needs careful interpretation within the principles of thermodynamics. Roldán stresses that their definition stays consistent with classical thermodynamics while revealing new possibilities through information processing.

"We use the classical definition of efficiency, that is, the fraction of the work extracted per cycle divided by the heat intake per cycle, both averaged over many runs of the machine," he clarified.

"We show that such a fraction can exceed the Carnot value in the GCE, and reach even one, corresponding to a 100% conversion of the heat intake into extracted work."

The distinction lies in accounting for the cost of information processing. While the thermal-to-mechanical conversion can exceed classical limits, the complete energy budget—including information acquisition and processing—respects fundamental thermodynamic constraints when fully considered.

"If we take into account for computing the efficiency the cost of erasure of the information about the particle position in each cycle, we come up with an alternative definition of efficiency that respects the Carnot limit," Roldán noted.

From theory toward laboratory reality

The researchers used realistic parameters from a previous experimental study.

"We are confident that our theoretical idea can be realized in the lab very quickly," Roldán stated. "All our numerical results were done using realistic experimental parameters that were taken from a previous work of ours, which realized the first ever Carnot machine with a polystyrene sphere trapped in optical tweezers."

The main experimental challenges involve high-speed position detection and rapid feedback implementation. The research reveals that sampling frequencies above 100 kilohertz are crucial; below this threshold, performance degrades significantly due to detection delays that prevent optimal timing of the zero-cost interventions.

"Our ideas, and similar ones in the emerging field of stochastic thermodynamics, are so far proof of concepts of what could inspire realistic designs of efficient nanomachines defying classical thermodynamic limits," Roldán explained.

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