Abstract
Maxwell’s demon is an entity in a 150-year-old thought experiment that paradoxically appears to violate the second law of thermodynamics by reducing entropy without doing work. It has increasingly practical implications as advances in nanomachinery produce devices that push the thermodynamic limits imposed by the second law. A well-known explanation claiming that information erasure restores second law compliance fails to resolve the paradox because it assumes the second law a priori, and does not predict irreversibility. Instead, a purely mechanical resolution that does not require information theory is presented. The transport fluxes of mass, momentum, and energy involved in the demon’s operation are analyzed and show that they imply “hidden” external work and dissipation. Computing the dissipation leads to a new lower bound on entropy production by the demon. It is strictly positive in all nontrivial cases, providing a more stringent limit than the second law and implying intrinsic thermodynamic irreversibility. The thermodynamic irreversibility is linked with mechanical irreversibility resulting from the spatial asymmetry of the demon’s speed selection criteria, indicating one mechanism by which macroscopic irreversibility may emerge from microscopic dynamics.
Highlights
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The demon’s sorting mechanism is passive—the original gas demon merely allows molecules to pass from one side of a box to the other if they satisfy some selection criterion, but blocks their passage in the reverse direction— there is no obvious means of external entropy generation available, and the demon appears paradoxically to be able to circumvent the second law and generate free energy without doing work [4,5]
The paradox is resolved by a more concrete route that does not depend on information theory or Landauer’s principle, does not assume the demon obeys the second law a priori, and yields a quantitative lower bound on entropy production by the demon
Summary
“Maxwell’s demon” refers to a class of thought experiments that probe the universality of the second law of thermodynamics. The sorting mechanism is assumed to be passive in the sense that it does not change the energy or momentum of particles that it allows to pass from one chamber to the other, while particles that it blocks are reflected elastically as from a perfectly rigid wall This is in the spirit of the original thought experiment, in which Maxwell was concerned only with the temperature difference and deliberately designed his demon not to alter the state of the particles it chose to let pass. Where Uis the rate of change of the internal energy of the gas, Kis the rate of gain of kinetic energy of the beam, that is, the rate of energy transport out of the emitter and into the receiver, Wmech is the rate of doing mechanical work on the subsystem by the external force, that is, by the demon, Wchem is the rate of doing chemical work associated with temperature (discussed below), Qdiss is the rate of external heat dissipation, and primes indicate the corresponding quantities at the receiver (Figure 2). While this assumption limits the generality of our result, it allows the result to be expressed in terms of the temperatures of the gases and makes the interpretation of the dissipation mechanism derived below more transparent
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