# Maxwell's demon - Landauer's principle and it's incompatibility with the 1st law of thermodynamics

Let's recapitulate and state both the Maxwell's demon and the official most-widely accepted solution to the paradox, namely Landauer's principle:

A demon just by observing But Never Touching -hence no energy is transferred- the molecules of two chamber of gas separated by a door, opening and closing the door between the two sides at the right moments can create a temparature difference, therefore creating an entropy decrease, which can be used to do useful work, thus violating the Second Law of Thermodaynamics.

2. Landauer's principle the officially accepted solution to the paradox:

Not when the Demon acquires the information about the molecules of the gas, but when erases the accumulated information the Demon's memory offsets the created entropy decrease and amount of work extracted by an amount of dissipated heat-energy at least as much as much useful work was done by the action of the demon. Therefore the dissipated heat to the environment offsets the entropy decrease created by the action of the demon, thus the Second Law of Thermodynamics is preserved.

The problem: This is a so horribly shallow superficial explanation, that barely stands until said. Because let's see:

• It is not mandatory to extract the created temperature difference into useful work, we can decide to stop the demon to do it's job, keep the information in the memory, and just to let the two sides to come back to thermal equilibrium, and because we settled on the conditions that the Demon doesn't exchange any energy with the molecules, the total energy is the same constant all the time, but if we now ask the Demon to erase it's memory, still has to dissipate heat-energy to the environment, because this is also settled in Landauer's erasure principle, but in this way energy is created on the top of already total constant energy, so the Conservation of Law of Energy (1st law of thermodynamics) is violated. Of course with this example can be seen that by applying Landauer's principle, and dissipate heat on erasure the 1st Law of Thermodyanics - the conservation of energy - is violated all the time, no matter what order the things are done.