Can the Second Law of Themodynamics Be Violated?

Can you imagine an egg which unscrambles? Or a jet engine that takes ambient heat and exhaust fumes to generate kerosene and oxygen? I suppose you can't. In physics, the Second Law of thermodynamics, establishes that it is not going to happen. In this post I explain the second law of thermodynamics and discuss whether it can be violated or not.

This post is part of the initiative "El Carnaval de la física" (the physics carnival), created by the blog Gravedad Cero and promoted by the Unione Astrofili italiani to commemorate the first observation of a heavenly object by Galileo.

Second Law

Entropy can be seen as a measure of the disorder of a system, the more entropy, the more disordered the system is. Technically, entropy is the measure of the number of microscopic states that give the same macroscopic properties.

The Second Law of thermodynamics states that the entropy of an isolated system which is not at equilibrium will tend to increase, reaching its maximum value in the equilibrium state, this means that its macroscopic properties such as temperature or pressure remain stationary. Another way to state this principle, equivalent to the first one, is that it is impossible to convert heat into work in a cycling process. You cannot take heat from a high-temperature source and completely convert it into work without transferring some heat to a low-temperature energy sink. Unlike the laws of mechanics, where time can go forward and backward, the second law of thermodynamics gives a privileged time direction. There are irreversible processes.

But some nanomachines, like mitochondria in cells which are far from equilibrium, spent some of their time working in reverse (like the jet engine which converts ambient heat into kerosene!). How can this happen? Do they break the second law? Does the second law fail when we go to the realm of "very small"? Is the second law only a statistical one? To find the beginning of the dicussions about the second law, we must travel backward in time, to the nineteenth century.

Maxwell Demons

Physicists have been dealing with the Second Law of thermodynamics since 1871 when James Clerk Maxwell, in his Theory of heat introduced a small creature to show that the second law is a statistical one. That creature has been known since then as the Maxwell Demon. The Maxwell Demon is a demon small enough to see the single molecules of a gas, such as the one in the image below. This Demon is situated in a container divided by a wall into two parts, A and B, filled with the same gas at the same temperature. When a molecule faster than the average in the A part of the container is close to the wall, the Demon opens a trap and the molecule will go to the B compartment. As the temperature is an average of the velocity of the individual molecules, if the demon repeats this process many times, the temperature will increase in B and decrease in A without any cost of energy.

This game, simple at a first look, has upset physicists, who tried to find a solution and to improve the Maxwell Demon to put to the test the Second Law. In this case, the contradiction vanishes if the Demon is taken into account as part of the system. The entropy produced for the Demon, when he tries to measure the information of the molecules, is higher than the entropy lost for the gas system.

(credits for image go to: Волобуев, Wikimedia Commons)

One of more important responses to the Maxwell Demon was the response given by the physicist Léo Szilard in 1929 in the published article, On the Decrease of Entropy in a Thermodynamic System by the intervention of Intelligent Beings. The Szilard engine is a variation of the Maxwell Demon which consists in a single particle gas in a cylinder at a thermal bath at temperature T. The cylinder has a piston that separates it in two halves. If the Demon knows in which part the particle is, he can let the gas expand reversibly and then remove the piston. With the expansion, the gas performs work, which is taken from the external bath. The engine extracts energy from a single thermal bath! Szilard's argument was that the amount of energy necessary to know in which part of the cylinder the particle is, would be greater than the amount of work produced by the Szilard engine. But Szilard was not precise in this part of the work, he didn't calculate the exact amount of energy the demon would need because his first premise was that the second law could not be broken. Later, some physicists tried to calculate this energy more precisely, like Léon Brillouin. He argued that, in order to see a molecule, it is necessary that this molecule scatters at least one photon whose energy dissipation would produce an increase of entropy at least equal to the decrease produced by the Szilard engine.

An interesting fact about the different kinds of Maxwell Demons is that they showed the relationship between information and thermodynamics entropies. In 1982, Charles H. Bennett demonstrated that, even if some measurement processes do not need energy, erasing information does and a Demon will eventually need information space. An easy-to-understand article about Maxwell Demons and information theory was published in 1987 in Scientific American by Charles H. Bennett and is called Demons, Engines and the Second Law. In 2004 J.M. Parrondo published the article Entropy, macroscopic randomness and symmetry breaking phase transitions, which can be interesting for those familiar with physics. In this article a macroscopic Szilard Engine was constructed, but it does not violate the second law.

Fluctuation Theorem

But I started the article talking about engines that actually work "in reverse", what has happened with them? How can Thermodynamics deal with that? To answer that I must explain the Fluctuation theorem. The fluctuation theorem, originated from statistical mechanics, shows that the second law is only a statistical one and quantifies the probability of an isolated system to decrease its entropy. It states that, with the increasing of time and the size of the system, the probability of seeing an entropy production contrary to the second law decreases exponentially. This is not against the second law because the second law is considered a time average of the entropy production.

A violation of the second law on the level of thousands of atoms and molecules and appreciable time scales was reported for the first time in 2002. The original article by G.M. Wang et al, from the Canberra and Brisbane Universities was published in the issue 89 of Physical Review letters, Experimental Demonstration of Violations of the Second Law of Thermodynamics for Small Systems and Short Time Scales. In the experiment, the trajectories of some latex beads captured in a optical trap and suspended in water are measured at short time-scales, consequently the change in entropy of the system can also be calculated. The researchers found that, in intervals of few tenths of seconds, the change in entropy can be negative, the bead was gaining energy from the surrounding water. But when time is over two seconds, a positive entropy change was measured. This experiment has been considered the first experimental evidence of the Fluctuation Theorem and was widely reported, for example in Nature News or in New Scientist.

Fèlix Ritort presented at the 2003 Poincaré Seminar an article about the state of the art and future perspectives of the second law transient violations entitled Work fluctuations, transient violations of the second law and free energy recovery methods: Perspectives in Theory and Experiments. This paper, after a technical explanation about second law and work fluctuations, gives some examples where transient violations are expected. According to Felix Ritort, many biomolecules are expected to show transient violations, like DNA or RNA polymerase during the replication and transcription processes, or like ribosomes. But two main problems arise in the experiments of single molecules: accuracy and reproducibility. Few single molecule experiments are reproducible, especially if the experiment involves some biomolecular process.
One interesting example is the fluctuations observed in unfolding small RNA molecules under the action of a mechanical force.

Imagine you have a friend convinced that the Second Law can be broken. What would you say to him? Would you encourage him? I'm skeptical about the violations of the second law, but I hope many interesting demons, engines and experiments will be proposed in the future.