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.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.

American Journal of PhysicsFeb 1, 199012 citations

Concerning the Entropy Expression of the Uncertainty Principle

D. A. Bochvar, И. В. Станкевич, Anatolii L. Chistyakov

Soviet physics. DokladySep 1, 19631 citation

General fine-grained uncertainty relation and the second law of thermodynamics

Li-Hang Ren, Heng Fan

We investigate the fine-grained uncertainty relations for qubit systems by measurements corresponding respectively to two and three spin operators. Then we derive the general bound for a combination of two probabilities of projective measurements in mutually unbiased bases in $d$ -dimensional Hilbert space. All of those uncertainty inequalities can be applied to construct different thermodynamic cycles such that the violation of those inequalities will lead to the violation of the second law of thermodynamics. This reveals the relationship between fine-grained uncertainty and the second law of thermodynamics.We investigate the fine-grained uncertainty relations for qubit systems by measurements corresponding respectively to two and three spin operators. Then we derive the general bound for a combination of two probabilities of projective measurements in mutually unbiased bases in $d$-dimensional Hilbert space. All of those uncertainty inequalities can be applied to construct different thermodynamic cycles such that the violation of those inequalities will lead to the violation of the second law of thermodynamics. This reveals the relationship between fine-grained uncertainty and the second law of thermodynamics.

arXiv:1312.6744Physical Review ANov 14, 201411 citations

Violation of the 2nd law of thermodynamics in the quantum microworld

Vladislav Čápek, O. M. Frege

Czechoslovak Journal of PhysicsMay 1, 20021 citation

d

-dimensional Hilbert space. All of those uncertainty inequalities can be applied to construct different thermodynamic cycles such that the violation of those inequalities will lead to the violation of the second law of thermodynamics. This reveals the relationship between fine-grained uncertainty and the second law of thermodynamics.