Reaction Kinetics Based on Time-Energy Uncertainty Principle

Rafael D. Sorkin

Harvey S. Leff

What rate (Pd) of energy transfer is attainable by a Maxwell’s demon who sorts gas molecules serially; and how much time (td) does it take to achieve a designated temperature difference ΔT across a partition? Two estimates are made, using (i) the energy–time form of Heisenberg’s uncertainty principle and (ii) classical kinetic theory. For a dilute gas, at ∼300 K, the uncertainty principle implies Pd <1.5×10−6 W. If the gas volume is the size of a large room, and ΔT=2 K, then td >103 years. These bounds are loose, but are of interest because this is one of few elementary applications of the energy–time uncertainty principle. With similar assumptions, classical kinetic theory implies much tighter bounds: Pd <10−9 W and td >4×106 years. The kinetic theory approach allows an extension of Brillouin’s demonstration that the second law of thermodynamics cannot be violated by a Maxwell’s demon using light signals.

Iwao Yasumori, Kenji Fueki

Alexander D. Sukhanov

Yu. E. Kuzovlev

1/f noise at arbitrary low frequences is the way of existence of irreversibility in thermal motion governed by reversible laws of mechanics. This statement not once was confirmed in statistical mechanics beyond its traditional kinetical roughenings. Here we point out that in case of quantum statistical mechanics in principle it is sufficient to avoid such the roughening as the "Fermi golden rule". This means taking into account the time-energy uncertainty principle (time-frequency one in classical limit) and thus uncertainties in characteristics of real collisions and scatterings of particles and/or quanta. We consider the resulting "pseudo-kinetics" and demonstrate how it produces quantum 1/f-noise

Yu.I. Vorontsov