Entropy (also known as the second law of thermodynamics) is a hard mistress. If you think of the universe as a cosmic casino, the laws of thermodynamics boil down to the house edge: you can’t win, you can’t break even, and – if you don’t open a portal to an alternate universe with different physical laws – you can’t get out of the game. You just have to keep playing and hopefully come up with successful strategies to minimize your losses as much as possible – and maybe even get ahead once in a while, at least in the short term.
That’s the gist of a new paper published in the journal Physical Review Letters. The paper updates a classic 19th-century thought experiment known as Maxwell’s demon, which offers a potential loophole to undermine the second law — at least temporarily. Now physicists have proposed a gambling version of the demon playing a slot machine, unable to control when the machine pays out (in terms of free energy available for work), but able to choose when to stop playing. to maximize ‘profit’. The research could one day lead to improved efficiency of microscopic heat engines and motors.
As we reported earlier, around 1870 James Clerk Maxwell envisioned a small gnome who was able to put order in a closed container filled with gas. The imp achieved this by flowing heat from a cold compartment to a hot compartment, which apparently violates the second law. The two compartments would be separated by a wall with a hatch covering a hole just large enough for a gas molecule to pass through.
Maxwell’s hypothetical imp would sit on top of the dividing wall and open and close the hatch at will. Gas molecules would generally be highly disordered (high entropy), in the sense that they have approximately the same average velocity and temperature and would therefore be close to equilibrium. So there wouldn’t be much energy available for “work” – defined in physics as the force over a certain distance (W=fd†
Since the atoms that make up the molecules are in constant motion, there will be small fluctuations over time. Whenever the demon sees a molecule moving slightly faster near the hole in the right (cold) compartment, it will open the shutter and let the molecule through to the left (hot) compartment. The imp does the same for all slow-moving gas molecules in the left compartment, allowing them to get into the colder right compartment. So the molecules in the left compartment get hotter and hotter, while those in the right compartment get colder and colder, in an apparent reversal of entropy. Once you have that temperature difference, you basically have a heat pump that can do useful work.
Statistically, of course, it is nearly impossible to sort and separate billions of individual molecules by speed or temperature. In principle, an enormous amount of extra energy would be required. Maxwell’s demon provides that extra energy, so the thought experiment is not a true closed system and there is no violation of the second law.
Physicists have devised some pretty clever experiments to bring some version of the demon into the lab. For example, in 2007, Scottish scientists devised an “information ratchet” to create a temperature difference in chemical systems that would otherwise be in thermal equilibrium. The following year, researchers at the University of Oregon came up with an ingenious version that involved using laser light to create a box, with two other lasers serving as a trap door and a “demon,” respectively.
Japanese physicists discovered how to lure a nanoscale bead onto a spiral staircase in a 2010 paper in Nature, based on Szilard’s concept of the motor. In 2013, German scientists built an experimental equivalent of Maxwell’s demon from a pair of interacting quantum dots (tiny pieces of semiconductors just a few nanometers wide). And in 2018, Penn State physicists rearranged a random array of atoms into organized blocks to create a quantum equivalent of Maxwell’s demon.
For this latest paper, co-author Gonzalo Manzano of the International Center for Theoretical Physics (ICTP) in Trieste, Italy, and his colleagues wondered if they could come up with a strategy that didn’t require the high degree of control of the original thought experiment. . , while the demon can still create that all-important asymmetry to harvest energy for work. In this new version, the microscale demon can only passively observe as the shutter opens and closes automatically and unpredictably. Depending on whether hot and cold particles are successfully separated with each opening and closing of the shutter, the demon must choose whether to keep “playing” the game or stop and start over.
Essentially, the demon bets on the outcome of a molecular-scale slot machine, deciding after each spin whether to continue playing or stop. Each turn incurs a work cost, similar to the cost of each spin. The gambling demon must determine the best strategy to achieve a temporary net gain in his energy gain by taking advantage of the occasional random fluctuations in the movement of the particles. “One way to develop successful strategies is to stop when things somehow ‘get bad’ to avoid big losses,” Manzano told APS Physics.
manzano et al† discovered that there was not one successful strategy: some “stop” strategies were successful and others were not. Even the successful ones only worked in the short term. Play the game long enough, and entropy always wins in the end. The authors found that the key to obtaining a temporary net energy gain for a given run is to ensure that the sequence of opening and closing of the shutter breaks the time-reversal symmetry (consistent with the arrow of time that exists in our existence. mastered on a macro scale).
This was confirmed by an experimental nanoelectronic device the team set up with the help of physicist Jukka Pekola of Aalto University, in which some electrons tunnel into a metallic island. As Philip Ball wrote at APS Physics:
[The device] consists of electrodes separated from a metal island by an opening. When cooled to a fraction of a degree Kelvin, individual electrons can jump between the island and the electrodes. A voltage on the island controls the chance of jumping and thus acts as a hatch. When an electron jumps onto the island, the heat withdrawn from the electrode can be converted into work; conversely, when an electron jumps from the island to an electrode, heat is dissipated.
An approach like the gambling demon could one day improve the performance of micromotors such as thermal ratchets. The researchers argue that their gambling demon should also function in the quantum realm, raising the possibility that quantum devices can temporarily beat the second law to extract work from random quantum jumps.
DOI: Physical Review Letters, 2021. 10.1103/PhysRevLett.126.080603 (About DOIs).