I am possessed! Yes, with the thinking that if there is actually a Maxwell's Demon, then it would open the negligible weighted door which would ultimately make the second law invalid. But really can second law be invalid? This is not my question. It is a universal law. So, what should be the logic that the Demon would fail?? Please don't say that work must be done to open the door. The door is so light that negligible work is done.
Answer
The resolution to Maxwell's demon paradox is mostly understood to be through Landauer's principle, and it is one of the most compelling applications of information science to physics. Landauer's principle asserts that erasing information from a physical system will always require performing work, and particularly will require at least $$k_B T \ln(2)$$
of energy to be spent and eventually released as heat. The concept of 'erasing information' is relatively tricky, but there are some pretty solid foundations to think that this principle is right.
To apply it to the demon, you should realize that the demon consists of (at least) two parts: a sensor to detect when particles are coming, and an actuator to actually move the door. For the demon to work correctly, the actuator must act on the current instruction from the sensor, instead of the previous one, so it must forget instructions as soon as a new one comes in. This takes some work: there is some physical system encoding a bit and it will take some energy cost to flip it.
Now, there are some criticisms of Landauer's principle, and it is not completely clear whether it is dependent on the Second Law of Thermodynamics or if it can be proved independently; for an example see this paper (doi). Nevertheless, even if it is a restatement of the Second Law, it carries considerable explanatory power, in that it clarifies how the Second Law forbids the demon from operating.
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