May 6, 2017


What Happens When You Mix Thermodynamics and the Quantum World? A Revolution (NATALIE WOLCHOVER, 05.06.17, Wired)

[O]ne of the strangest things about the theory is that these rules seem subjective. A gas made of particles that in aggregate all appear to be the same temperature--and therefore unable to do work--might, upon closer inspection, have microscopic temperature differences that could be exploited after all. As the 19th-century physicist James Clerk Maxwell put it, "The idea of dissipation of energy depends on the extent of our knowledge." [...]

In an 1867 letter to his fellow Scotsman Peter Tait, Maxwell described his now-famous paradox hinting at the connection between thermodynamics and information. The paradox concerned the second law of thermodynamics--the rule that entropy always increases-- which Sir Arthur Eddington would later say "holds the supreme position among the laws of nature." According to the second law, energy becomes ever more disordered and less useful as it spreads to colder bodies from hotter ones and differences in temperature diminish. (Recall Carnot's discovery that you need a hot body and a cold body to do work.) Fires die out, cups of coffee cool and the universe rushes toward a state of uniform temperature known as "heat death," after which no more work can be done.

The great Austrian physicist Ludwig Boltzmann showed that energy disperses, and entropy increases, as a simple matter of statistics: There are many more ways for energy to be spread among the particles in a system than concentrated in a few, so as particles move around and interact, they naturally tend toward states in which their energy is increasingly shared.

But Maxwell's letter described a thought experiment in which an enlightened being--later called Maxwell's demon--uses its knowledge to lower entropy and violate the second law. The demon knows the positions and velocities of every molecule in a container of gas. By partitioning the container and opening and closing a small door between the two chambers, the demon lets only fast-moving molecules enter one side, while allowing only slow molecules to go the other way. The demon's actions divide the gas into hot and cold, concentrating its energy and lowering its overall entropy. The once useless gas can now be put to work.

Maxwell and others wondered how a law of nature could depend on one's knowledge--or ignorance--of the positions and velocities of molecules. If the second law of thermodynamics depends subjectively on one's information, in what sense is it true?

A century later, the American physicist Charles Bennett, building on work by Leo Szilard and Rolf Landauer, resolved the paradox by formally linking thermodynamics to the young science of information. Bennett argued that the demon's knowledge is stored in its memory, and memory has to be cleaned, which takes work. (In 1961, Landauer calculated that at room temperature, it takes at least 2.9 zeptojoules of energy for a computer to erase one bit of stored information.) In other words, as the demon organizes the gas into hot and cold and lowers the gas's entropy, its brain burns energy and generates more than enough entropy to compensate. The overall entropy of the gas-demon system increases, satisfying the second law of thermodynamics.

The findings revealed that, as Landauer put it, "Information is physical." The more information you have, the more work you can extract. Maxwell's demon can wring work out of a single-temperature gas because it has far more information than the average user.

But it took another half century and the rise of quantum information theory, a field born in pursuit of the quantum computer, for physicists to fully explore the startling implications.

Over the past decade, Popescu and his Bristol colleagues, along with other groups, have argued that energy spreads to cold objects from hot ones because of the way information spreads between particles. According to quantum theory, the physical properties of particles are probabilistic; instead of being representable as 1 or 0, they can have some probability of being 1 and some probability of being 0 at the same time. When particles interact, they can also become entangled, joining together the probability distributions that describe both of their states. A central pillar of quantum theory is that the information--the probabilistic 1s and 0s representing particles' states--is never lost. (The present state of the universe preserves all information about the past.)

Over time, however, as particles interact and become increasingly entangled, information about their individual states spreads and becomes shuffled and shared among more and more particles. Popescu and his colleagues believe that the arrow of increasing quantum entanglement underlies the expected rise in entropy--the thermodynamic arrow of time. A cup of coffee cools to room temperature, they explain, because as coffee molecules collide with air molecules, the information that encodes their energy leaks out and is shared by the surrounding air.

Understanding entropy as a subjective measure allows the universe as a whole to evolve without ever losing information. Even as parts of the universe, such as coffee, engines and people, experience rising entropy as their quantum information dilutes, the global entropy of the universe stays forever zero.

Renato Renner, a professor at ETH Zurich in Switzerland, described this as a radical shift in perspective. Fifteen years ago, "we thought of entropy as a property of a thermodynamic system," he said. "Now in information theory, we wouldn't say entropy is a property of a system, but a property of an observer who describes a system."

The system being a property of the observer.

Posted by at May 6, 2017 8:40 AM