Maxwell: Thermodynamics Meets the Demon

Maxwell: Thermodynamics meets the demon
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A research team at the University of Maryland has published a mathematical model that could turn Maxwell's dream of order into a reality. Things get messier: Your office, the universe, even the air and dust in a room will become increasingly disorganized unless you or some cosmic force expends energy to clean it all up.

A brief history of thermodynamics

This pesky fact of life — that disorder, or entropy, increases over time — is known as the second law of thermodynamics. The machine they envision could transfer hot and cold particles between two chambers, thus decreasing entropy, just as Maxwell had imagined. Yet the device would obey the second law of thermodynamics because it would be self-contained, with no need for an outside power source.

Instead, it would need only a supply of bits — 0s and 1s — with which to encode information about the particles. Not so devilish after all.

Maxwell's Demon Meets Quantum Dots

If such a machine could increase order without outside power, could it be an infinite supply of energy? To avoid this, a pressure release valve was added which would open when the pressure reached a certain point. This level was set by hanging weights on a lever which came out from the valve. Papin saw that the weight was moved rhythmically up and down as the pressure rose up and was released. He realised that this power could be harnessed and was inspired to create a design for a piston and cylinder steam engine.

But it was Thomas Savery who ended up building the first engine, designed to raise water from mines. But all of these engines were very inefficient. Sadi Carnot wanted to be able study these problems in a scientific and mathematical way. This paper marked the start of thermodynamics as a science. They worked by exploiting the difference in temperature between the thermal energy created by burning fuel and the cool air outside. The fuel source and the cold air outside are both heat reservoirs — sources which are able to maintain their temperature.

Carnot imagined an engine using some particular cycle for doing work using a difference in temperature. He knew that this engine would have a certain efficiency for the difference in temperature between the two reservoirs.

3D grids of super-cooled atoms could one day form the basis for a quantum computer.

But it could also be run backwards: if the same amount of work was done in reverse spinning the wheel backwards the engine would return to its initial conditions, the ejected heat would be put back into the hot reservoir. Carnot defined the efficiency of this reversible engine, for a particular temperature difference, as X.

However he realised that this more efficient engine, were it to exist, would allow perpetual motion.

If you connected both of the engines to the same heat reservoirs you could use the more efficient one to do an amount of work Y. You could then use some of this work on the reversible engine, running it backwards, putting heat X back into the hot reservoir and restoring the initial conditions.

Order & Disorder: The Story of Information -Maxwells Demon

But since Y is greater than X, some energy will be left over after restoring the initial conditions. This would allow for perpetual motion, but Carnot said that ideas of perpetual motion were inconsistent with our experience of the Universe and so concluded that any engine more efficient than a reversible engine was physically impossible.

This was useful because it made a reversible engine the ideal engine. As we decrease heat losses can get closer and closer to it but we can never make an engine more efficient than a reversible engine. Since a particular force is needed to counteract gravity. Although Carnot had discovered great things he had done it all using an outmoded theoretical model of temperature called the Caloric Theory.

It flowed from hotter bodies to cooler ones, travelling in and out through pores in the material. The theory was quite successful; it could explain why two bodies of different temperatures left in contact with each other reached the same temperature. The caloric spread out as much as it could due to its repulsion, so the high concentration in the hot body moved out into the cold body where there was less caloric. The caloric theory however slowed down progress because the fact that work could be converted into heat and vice-versa was not fully realised.

This idea was proposed, all but simultaneously, by three scientists working independently during the s. But it was James Prescott Joule who would eventually give his name to the unit of work. Joule used a number of methods to heat water from spinning a paddle wheel powered by a falling weight to using an early electrical cell.

He found that the work needed to achieve a particular temperature rise was very similar for all of these disparate methods and caclulated a value for it, which we now know as the specific heat of water. All this research pointed to the idea that energy was neither created nor destroyed but converted into various forms.

This only applies in an adiabatic process — one in which no heat is transferred to or from the system. This law is simple, and perhaps seems obvious. But it creates an entirely new concept, the idea of entropy. The second law states that, if unhindered, localised energy tends to spread out. A cup of tea will dissipate its heat to the atmosphere and slowly cool. Air will rush out of a tyre when it is punctured, but will not when it is prevented from doing so by the tyre rubber. From this we can see why Entropy must increase. Let us take the simple example of a block of ice, weighing 2 kg, sitting in a bowl in a room at K room temperature.

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The block of ice is a system and the room is a system. We know that in these circumstances the ice will melt, but that doing so will require an energy input. We know that this is the energy q transferred to the block of ice from the air in the room. We have calculated entropy change. We just divide the energy transferred by the temperature of the air K. The important result here is that we have a positive number. Though one thermodynamic system has lost energy and another has gained it the net result has been an increase in entropy.

You know what would happen, heat only flows from hotter bodies to cooler bodies, the energy change would be in the opposite direction, the ice would warm the air. It is at this point that James Clerk Maxwell appears on the scene. In , following great discoveries about electromagnetics, Maxwell turned his attention to gases. In Daniel Bernoulli had suggested that pressure exerted by a gas might be caused by the gas molecules continually crashing into each other, and the walls of the container, at very high speed.

But since the ideas of conservation of energy had not yet been accepted people struggled to see how gas molecules could collide without slowing down at every collision.

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Where k is the Boltzmann constant, T is the absolute temperature in Kelvin and m is the molecular mass of the gas. Three graphs of this probability distribution at different temperatures are shown at the right. The probability is highest at a particular point, the most likely speed, which is associated with the temperature. But on either side of this point there are many molecules with lower and higher speeds. In a gas some molecules will have speeds in the thousands of ms -1 and others speeds just above 0.

The area under each of the curves is 1, because this is a distribution of probabilities and every possibility must be accounted for, and this explains the lower curves for higher temperatures. Very significantly, this distribution could also predict the second law of thermodynamics. Suppose you have a hot substance with many fast moving molecules and you bring it into contact with a cold substance containing slow moving molecules.

Viewpoint: Maxwell’s Demon Meets Nonequilibrium Quantum Thermodynamics

The fast molecules will hit the slow molecules accelerating them, as they do this they will slow down. What was so revolutionary about this? After all, the two theories agreed with each other. The difference was that the Maxwell-Boltzmann distribution was, unashamedly, just a statistical distribution. It was what was most likely to happen. But just occasionally every single molecule in the hot substance might be hit from the side by a molecule in the cold substance. This would mean heat flowing from cold to hot. For we have seen that molecules in a vessel full of air at uniform temperature are moving with velocities by no means uniform, though the mean velocity of any great number of them, arbitrarily selected, is almost exactly uniform.

Now let us suppose that such a vessel is divided into two portions, A and B, by a division in which there is a small hole, and that a being, who can see the individual molecules, opens and closes this hole, so as to allow only the swifter molecules to pass from A to B, and only the slower molecules to pass from B to A.

He will thus, without expenditure of work, raise the temperature of B and lower that of A, in contradiction to the second law of thermodynamics. The demon watches molecules bouncing around in a box and opens a trapdoor to allow fast molecules from A to B and slow molecules from B to A. All the demon has done is to watch the particles and open a trapdoor. If this trapdoor is frictionless we can perhaps imagine him doing no work at all. There are a number of serious problems here. The second law of thermodynamics has been violated. All the way through the sorting process heat has been passing from a colder gas to a hotter one.

This has major implications. Once we have sorted the molecules like this we can put a turbine by the trapdoor and open it. Molecules in B will move to A, spinning the turbine and doing work. We could extract all of the thermal energy of molecules in a single reservoir until they almost come to a standstill by cycling between the use of a demon and a turbine. We would then have brought the temperature of the gas down to close to absolute zero. We would have done all this without using energy but in fact in the process of getting energy.

You may ask how the door can open without work being performed on it. But we model the movement of the door as a quasistatic process, meaning that it happens infinitely slowly. They also show that the amount of entropy production is in excellent agreement with models of nonequilibrium thermodynamics that account for both thermal and quantum fluctuations [ 6 ] and the feedback control mechanism [ 7 ].

The techniques employed by the authors in this work could be used to help control and enhance the performance of the thermal machines of the future. And when combined with current progress in machine learning, studies such as this promise to inspire a new era of what one might call quantum cybernetics. This research is published in Physical Review Letters. His interests and work range from many-body physics to quantum information and the thermodynamics of quantum systems. Following a doctorate in from University College Cork, Ireland, he moved, as a research fellow, to the Center for Quantum Technologies at the University of Singapore, and then as a Marie Curie Fellow to the University of Oxford, England, between and , after which he moved to Trieste.

In Dublin he will focus on building a group aimed at understanding the stochastic energetics of small and large nonequilibrium quantum systems. Patrice A. Camati, John P. Peterson, Tiago B. Souza, Roberto S. Sarthour, Ivan S.