The discussion centers on the theoretical implications of Maxwell's Demon in relation to the uncertainty principle and the second law of thermodynamics. Participants explore how a hypothetical Maxwell's Demon could measure the position and velocity of particles without violating the uncertainty principle. The conversation emphasizes that while the demon's existence is not real, its implications can be analyzed through classical and quantum mechanics frameworks, particularly using the Schrödinger equation and Hilbert space concepts. Calculating the limits imposed by the uncertainty principle on the demon's effectiveness is suggested as a valuable exercise.
PREREQUISITESThe discussion is beneficial for physicists, students of quantum mechanics, and anyone interested in the intersections of thermodynamics, information theory, and theoretical physics.
iVenky said:Maxwell's demon ... How can it do that
The logic of the Maxwell's Demon argument starts "If there were such a thing, then..." and considers the consequences of that assumption. That logic is valid whether or not such a thing can actually be created.iVenky said:Maxwell's demon measures the position and velocity of the particle. How can it do that when it violates the uncertainty principle?
So you are saying even within the limits of uncertainty, the demon could produce a detectable effect hypothetically?Nugatory said:The logic of the Maxwell's Demon argument starts "If there were such a thing, then..." and considers the consequences of that assumption. That logic is valid whether or not such a thing can actually be created.
(It woud also be a good exercise to calculate the actual limits the uncertainty principle places on the effectiveness of a hypothetical Maxwell's Demon. The demon doesn't have to sort every single atom that comes by, just enough to produce a detectable effect).
I'm saying that you should try calculating an upper bound for yourselfiVenky said:So you are saying even within the limits of uncertainty, the demon could produce a detectable effect hypothetically?
The Maxwell's demon (being real or not) is supposed to measure all initial data that, according to a given theory, completely determine the future evolution of the system. If the given theory is classical mechanics, then those initial data are positions and velocities of all particles. But if the given theory is quantum mechanics, then the initial data is the initial state in the Hilbert space, the future evolution of which is determined by the Schrödinger equation. The latter corresponds to a quantum Maxwell's demon, which is compatible with the uncertainty principle.iVenky said:Maxwell's demon measures the position and velocity of the particle. How can it do that when it violates the uncertainty principle? Does that mean uncertainty principle is unavoidable otherwise we will violate II law of thermodynamics as in the case of Maxwell's demon?