Gambling strategies for a microscopic world

The good gambler is the one who knows when to quit. This is not the first rule of “The Gambling Handbook”, but is what a team of ICTP scientists, together with international colleagues, learned from their latest experiment. The work featured a particular kind of gambler - a revised version of Maxwell’s demon who plays with a microscopic slot machine in the realm of thermodynamics.

The gambling demon is a thought experiment in which the imaginary being invests work (the equivalent of coins) on a non-equilibrium system (a metaphoric slot machine), hoping to obtain a positive payoff, that is, to hit a jackpot of free energy.

In Maxwell's original experiment, the demon is able to control a small door between two separate compartments filled with gas molecules. The demon has the ability to quickly open and close the door, to let fast molecules into one of the chambers, and slow molecules into the other. This will result in one chamber to warm up and the other to cool down, decreasing the entropy of the system and apparently violating the second law of thermodynamics.

In the paper “Thermodynamics of Gambling Demons”, recently published on Physics Review Letters, the authors propose a new version of the demon, one who is able to see the gas molecules like its more famous peer, but is not able to open and close the trapdoor at will. In this setting, the door opens and closes randomly and autonomously, and the only thing the demon can do is decide to stop the process, and eventually start it all over again, with the goal of inverting the spontaneous flow of heat.

The paper is the result of an international collaboration between a multidisciplinary group of scientists, including ICTP’s Condensed Matter and Statistical Physics (CMSP) section coordinator Rosario Fazio, and Quantitative Life Sciences (QLS) researcher Edgar Roldan. Gonzalo Manzano, the first author of the paper, was also a researcher in ICTP’s CMSP section, and is now working at the Institute for Quantum Optics and Quantum Information (IQOQI), at the Austrian Academy of Sciences, in Vienna, Austria. The theoretical approach by ICTP scientists was complemented by the experimental expertise of the PICO group laboratory at Aalto University in Finland, which implemented the setup to put the theory to the test.

“There is not an easy answer to what is the best strategy for our demon,” says Roldan. “It’s all about deciding when to stop the process. The demon gambles in the sense that it has to choose a strategy, let’s say, playing only three times, or stopping when it gets a specific result, and we tried to see which was more successful.”

“Compared to Maxwell’s demon, the gambler is not able to “apply feedback”, that is, to control the dynamics of the system,” adds Manzano, “but it has to wait for fluctuations that are beneficial for its purposes.”

Just like in a real-life casino, the demon relies on luck, but it has to cleverly decide to quit the game before it “gets bad”: in gambling, play long enough and you will certainly lose. “There is a time window in which the demon can hope to leave the table with some gain,” says Roldan. “It knows that if it waits until the end of the game it will lose; in fact, it is bound to lose by the second law.”

Apart from a clever gambling strategy, the authors also show that the gambling demon needs the condition that the system is not in a stationary state, in order to get a temporary energy gain. “This means that to be able to apply gambling strategies, we need a system that changes in time somehow,” says Manzano. “If the system is static, if it doesn’t change in time, even the best strategy in the world is not going to be successful.”

This was clearly visible in the experiment that the team set up in collaboration with physicist Jukka Pekola of Aalto University in Finland. “We were excited to work with them because they are experts in nano-electronics systems, and they could implement an incredibly precise experimental set-up,” says Roldan.

The device that implements the gambling demon scenario consists of electrodes separated from a small copper island by a gap. The island is maintained at a very low temperature (0.67 Kelvin) and electrons, coming from two aluminium leads can jump on and off. "In addition, a time-dependent voltage applied to the metallic island, performing work into the system, ensures that the system is not stationary," says Manzano. The applied voltage impacts the electrons and their chances of jumping. “When an electron jumps onto the island, heat extracted from the electrode can be converted into work; on the other hand, when an electron jumps from the island to an electrode, heat is dissipated and work is lost.” Thanks to the extremely low temperatures, the electrons can be counted one by one, making it possible for the researchers to collect important information from the system and to put their gambling strategies to the test. “Because the theory is so general, we could have tested it in many different experiments,” says Roldan, “but we chose this one because it's a very precise experiment that generates a lot of data. In this way, we could collect data for millions of fluctuations and we could really make good statistics.”

Roldan and Manzano say that during the peer review process of their paper, referees pointed out that their gambling demon could break the second law, thus threatening the whole field of thermodynamics. But just as in the original Maxwell demon thought experiment, the break of the second law is only apparent. “In order to gamble, our demon is acquiring information from the system, and this has a thermodynamic cost,” they explain. “When the demon quits a game, i.e., stops the process, its memory is somehow reset in order to play again. This loss of information has to be paid with work, so the second law is recovered.”

This gambling approach could have many applications, as for instance the optimization of energy extraction in thermodynamics or the performance improvement of microscopic motors and thermal machines. “We applied a tool from finance theories in thermodynamics, which is called Martingale theory,” says Roldan. “This is a very special mathematical tool and uncommonly used in physics, that allows us to discover new laws in thermodynamics. We think there is a long way to go and this is still the beginning of many new universal results for the field. We hope to have new developments, both theoretical and experimental.”

---- Marina Menga