Maxwell's Demon in Quantum Mechanics.

Orly Shenker,Meir Hemmo

doi:10.3390/e22030269

Abstract

Maxwell’s Demon is a thought experiment devised by J. C. Maxwell in 1867 in order to show that the Second Law of thermodynamics is not universal, since it has a counter-example. Since the Second Law is taken by many to provide an arrow of time, the threat to its universality threatens the account of temporal directionality as well. Various attempts to “exorcise” the Demon, by proving that it is impossible for one reason or another, have been made throughout the years, but none of them were successful. We have shown (in a number of publications) by a general state-space argument that Maxwell’s Demon is compatible with classical mechanics, and that the most recent solutions, based on Landauer’s thesis, are not general. In this paper we demonstrate that Maxwell’s Demon is also compatible with quantum mechanics. We do so by analyzing a particular (but highly idealized) experimental setup and proving that it violates the Second Law. Our discussion is in the framework of standard quantum mechanics; we give two separate arguments in the framework of quantum mechanics with and without the projection postulate. We address in our analysis the connection between measurement and erasure interactions and we show how these notions are applicable in the microscopic quantum mechanical structure. We discuss what might be the quantum mechanical counterpart of the classical notion of “macrostates”, thus explaining why our Quantum Demon setup works not only at the micro level but also at the macro level, properly understood. One implication of our analysis is that the Second Law cannot provide a universal lawlike basis for an account of the arrow of time; this account has to be sought elsewhere.

Highlights

We address in our analysis the connection between measurement and erasure interactions and we show how these notions are applicable in the microscopic quantum mechanical structure
In this paper we show that a Maxwellian Demon is compatible with standard quantum mechanics
As long as the Second Law is not assumed from the outset, there is no reason to think that the entropy of any subsystem in the setup should increase at the end of each cycle

Summary

Introduction

The “translation” of this idea to Gibbsian terms leaves out the essential magnitudes of this thesis, and the arguments for it; see [38] In his ground-breaking paper, Landauer [24] described his thesis in the classical context as follows. The same idea applies to the question of Maxwell’s Demon, which can be phrased roughly as follows: Can there be, as a matter of principle, a mechanical system (even highly idealized), and dynamical evolution that satisfy the laws of mechanics (quantum or classical), but violate the Second Law of thermodynamics? In appendix A we describe briefly the notion of a quantum macrostate

A Quantum

A Demon in Quantum Mechanics with the Projection Postulate

The Connection between Measurement and Erasure

Maxwell’s Demon