Maxwell's demon and the management of ignorance in stochastic thermodynamics

TL;DR

This paper explores how stochastic thermodynamics clarifies Maxwell's demon paradox by analyzing measurement, control, and information management in nanoscale systems, showing the second law's resilience against such hypothetical entities.

Contribution

It provides a detailed analysis of Maxwell's demon within stochastic thermodynamics, highlighting the constraints and limitations of control and information processing at small scales.

Findings

Demon fails because more work is needed for measurement than can be extracted.

Second law remains valid when considering average work and information costs.

Control constraints prevent indefinite violation of thermodynamic laws.

Abstract

It is nearly 150 years since Maxwell challenged the validity of the second law of thermodynamics by imagining a tiny creature who could sort the molecules of a gas in such a way that would decrease entropy without exerting any work. The demon has been discussed largely using thought experiments, but it has recently become possible to exert control over nanoscale systems, just as Maxwell imagined, and the status of the second law has become a more practical matter, raising the issue of how measurements manage our ignorance in a way that can be exploited. The framework of stochastic thermodynamics extends macroscopic concepts such as heat, work, entropy and irreversibility to small systems and allows us explore the matter. Some arguments against a successful demon imply a second law that can be suspended indefinitely until we dissipate energy in order to remove the records of his operations. In contrast, under stochastic thermodynamics the demon fails because on average more work is performed upfront in making a measurement than is to be extracted by exploiting the outcome. This requires us to exclude systems and a demon that evolve under what might be termed self-sorting dynamics, and we reflect on the constraints on control that this implies while still working within a thermodynamic framework.