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:

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*The Maxwell demon paradox:
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.


*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:

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*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.

I'm waiting for answers please.
Thank you
 A: I think, from the wording of the question, that you might not have understood the idea of Landauer's principle quite right. The principle asserts that if a system goes from one of two macroscopically distinct initial states to one and the same final state, by interacting with an environment which goes from its initial state to a final state described by the same set of macroscopic parameters (e.g. volume, temperature) in either case, then it must be that the entropy of the final state of the environment has gone up (because its macrostate now includes twice as many microstates as it did initially). Landauer then points out that in order to cause such a change in a thermal environment at finite temperature, one must supply not only entropy but also energy to the environment.
This principle does not assert that such an energy supplied to the environment is simply conjured up from nowhere, in violation of the first law. Rather, it has to be extracted from the system which is interacting with the environment. In the case of the Maxwell daemon, although no energy transfer is needed in order for the daemon to acquire information about microstates of a system, an energy transfer is required during the memory erasure. There is no contradiction between these two statements; they are two different processes.
