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Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics

Isothermal Maxwell demon as a quantum “sewing machine”

Vladislav Čápek

Published Apr 1, 1998• 21 citations
Publisher

Abstract

A model of an open microscopic quantum system interacting with an isothermal bath and able to bind actively particles from a reservoir to their even excited bound states at the cost of the bath energy is presented. The binding (potentially important in, e.g., chain reactions---hence ``sewing'') is due to dynamic processes in a central part of the system accompanying the particle transfer. The outcome thus challenges the second law of thermodynamics.

DOI
10.1103/physreve.57.3846

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A model of an open microscopic quantum system interacting with an isothermal bath and able to bind actively particles from a reservoir to their even excited bound states at the cost of the bath energy is presented. The binding (potentially important in, e.g., chain reactions---hence ``sewing'') is due to dynamic processes in a central part of the system accompanying the particle transfer. The outcome thus challenges the second law of thermodynamics.
A recently suggested simple model of an open microscopic system interacting with a bath and behaving like an isothermal Maxwell daemon is simplified and treated numerically. Results obtained confirm expectations that the system can, at the cost of thermal energy of the bath, spontaneously and in a cyclic process, pump particles from a particle reservoir to states with even higher energy. This contradicts the usual opinion based on the second law of macroscopic thermodynamics. For this effect, the interaction with the bath cannot be treated as weak. The role of dephasing owing to this interaction is illustrated.
With a class of quantum heat engines which consists of two-energy-eigenstate systems undergoing, respectively, quantum adiabatic processes and energy exchanges with heat baths at different stages of a cycle, we are able to clarify some important aspects of the second law of thermodynamics. The quantum heat engines also offer a practical way, as an alternative to Szilard's engine, to physically realize Maxwell's demon. While respecting the second law on the average, they are also capable of extracting more work from the heat baths than is otherwise possible in thermal equilibrium.
Maxwell's demon explores the role of information in physical processes.Employing information about microscopic degrees of freedom, this "intelligent observer" is capable of compensating entropy production (or extracting work), apparently challenging the second law of thermodynamics.In a modern standpoint, it is regarded as a feedback control mechanism and the limits of thermodynamics are recast incorporating information-to-energy conversion.We derive a trade-off relation between information-theoretic quantities empowering the design of an efficient Maxwell's demon in a quantum system.The demon is experimentally implemented as a spin-1=2 quantum memory that acquires information, and employs it to control the dynamics of another spin-1=2 system, through a natural interaction.Noise and imperfections in this protocol are investigated by the assessment of its effectiveness.This realization provides experimental evidence that the irreversibility in a nonequilibrium dynamics can be mitigated by assessing microscopic information and applying a feed-forward strategy at the quantum scale.
We now turn to the subject of thermodynamics, and to describing the process of thermalization of quantum systems. A quantum system that interacts with another system large enough to obey the usual rules of thermodynamics, is referred to as an open system. The thermal system with which it interacts is often referred to as a thermal bath , or simply as the environment. We will use these terms interchangeably. Modeling the behavior of open quantum systems has many applications. One of these is to model the noise that they are subjected to by their surroundings, noise that we will wish to control using measurement and feedback loops in Chapter 5. There are also two important connections between quantum measurements, information theory, and thermodynamics. The first of these is that the thermodynamic entropy of a macroscopic system can be identified with the information-theoretic entropy that characterizes the lack of knowledge of an observer about the microstates of the system. In turn, if an observer is allowed to make microscopic measurements on the system, then this modifies the thermodynamic rules regarding the conversion of heat to work. Such is the subject of Maxwell’s demon. Curiously it took more than a century to understand how Maxwell’s demon, essentially a microscopic measurement and feedback process, fits within the second law of thermodynamics. In another twist, it turns out that the process of erasing information requires an increase in the thermodynamic entropy of the environment, and this increase is directly related to the amount of information erased.
We present core ideas of quantum thermodynamics and a simple model of continuous quantum heat engines, relating their efficiency to the fundamental limit set by the Second Law. We apply a probability current analysis to these systems, allowing us to better understand their steady state behavior. Finally, we introduce a simple quantum mechanical model of Maxwell’s Demon—a system that extracts energy from a thermal reservoir at the cost of writing information to its memory—and analyze its behavior for a range of possible reservoir and memory tape parameters. We find that the information efficiency of our system is bounded by Landauer’s Principle and that it can approach this bound when its thermal reservoir and memory tape are nearly equally mixed.