The demon of Maxwell is a thought experiment proposed by James Maxwell in 1867 for violating the second law of thermodynamics.

Maxwell was interested in the kinetic theory of gases, where the properties were reduced thermodynamic thereof to the mechanics of a large number of molecules. The heat was then reduced to a particular form of energy in the form of disorderly agitation of the molecules. More unrest is more important the temperature of the gas being high.

But then, the science of energy conversion, including the rules of conversion of heat into usable work, thermodynamics, implies a direction to the passage of time and limits the possible transformations of energy and matter . The heat does not pass spontaneously from a cold body to a warm body, can not transform work if the temperature is the same everywhere in a system and a broken vase does not spontaneously glue or a drop of ink in a glass of water does not gather itself after running.

But if we take very seriously the reduction of thermodynamics to mechanics, this is more than ironic. The equations of motion of particles in a gas or is any other material body, do not differentiate between a movement in a sense of time and movement in the opposite direction. This means that there could be as much chance of breaking a vase than to see recoller spontaneously, or that the drop of ink diffusing in a glass returns to its initial state of concentration. The second principle is therefore true that, on average, approximately, and should therefore be violated even if it would, in practice, very difficult. Except of course for a similar Démon Laplace, ie the famous Maxwell demon!

If we imagine a box with the original molecules of a real gas gathered in a corner, the thermal agitation and thus the second law of thermodynamics, will this gas that will evenly distribute up to occupy the whole volume of the box. You will reach a situation known as equilibrium thermodynamics, where the gas n'exhibe no tendency to come together again in a small volume of the box. This allows to define a meaning for the passage of time.

Now imagine a wall separating the box into two parts, one B is larger than the other A. Part A corresponds to the initial area where the gas prior to broadcast. A small hole is drilled in the wall with a door a small daemon can close or open at will.

The gas is initially distributed uniformly in all parts of the box, when a molecule moves towards the hole, Part B to A, the demon leaves the door open. Conversely, if the molecule comes from A towards B, the daemon closes the door.

It is understandable that after a certain time, the gas will be back in a corner of the box and you will be returned to a situation of non-equilibrium. It therefore violated the second law of thermodynamics!