The Physics of Maxwell's demon and information (0707.3400v2)

Abstract: Maxwell's demon was born in 1867 and still thrives in modern physics. He plays important roles in clarifying the connections between two theories: thermodynamics and information. Here, we present the history of the demon and a variety of interesting consequences of the second law of thermodynamics, mainly in quantum mechanics, but also in the theory of gravity. We also highlight some of the recent work that explores the role of information, illuminated by Maxwell's demon, in the arena of quantum information theory.

• The paper demonstrates that acquiring and erasing information via Landauer’s principle imposes a fundamental energy cost, preserving the second law of thermodynamics.
• It employs Szilard's engine to quantify the minimum energy cost of kT ln2 per bit, linking classic thought experiments with modern quantum systems.
• The study highlights practical implications for quantum computing and thermodynamic system design by bridging information theory with physical energy constraints.

Review of "The physics of Maxwell's demon and information"

The paper "The physics of Maxwell's demon and information" by Koji Maruyama, Franco Nori, and Vlatko Vedral offers an extensive exploration of the profound interplay between information theory and thermodynamics, particularly through the lens of Maxwell's demon. This thought experiment, introduced by James Clerk Maxwell in the 19th century, challenges the second law of thermodynamics by postulating a hypothetical being that can seemingly decrease the entropy of a closed system without expending energy.

Summary of Key Concepts

Maxwell's demon has historically been pivotal in demonstrating the foundational principles of thermodynamics and information theory. The paper revisits the demon's paradox by examining classical and quantum systems, and reviewing how these thought experiments align with broader physical laws.

1. Maxwell's Demon and the Second Law:

The demon operates by sorting molecules in a gas to create a temperature gradient, ostensibly breaching the second law which posits that entropy within a closed system must not decrease. This paradox is addressed by acknowledging that the act of gaining information (or measurement) by the demon would inherently cost energy, thereby restoring compatibility with the second law through Landauer's principle.

2. Szilard’s Engine and Landauer’s Erasure Principle:

Szilard refined the concept by introducing a single-molecule gas engine that ties the demon's actions to information theory. Erasure of information is tied to a minimum energy cost of $kT \ln 2$ per bit, signifying a physical form of information processing underpinning quantum mechanics.

3. Modern Interpretations and Computational Aspects:

Contemporary research finds Maxwell's demon relevant in fields such as quantum computing and thermodynamic computations. The demon theoretically sets limits on computational efficiencies through specific thermodynamic costs for information erasure.

4. Quantum Mechanic Implications:

Maxwell’s demon extends into quantum mechanics, suggesting boundaries for state discrimination and hinting at constraints imposed by quantum coherence and entanglement. This line of inquiry potentially links information processing to the thermodynamic properties of quantum systems, inviting further exploration in areas like quantum state thermodynamics.

Numerical Insights and Claims

The authors discuss several experimental and theoretical constructs such as thermal randomization and quantum ratchets that reflect the physicality of information. They emphasize the critical energy-entropy relationship, backed by theoretical and empirical sources, and suggest entities like the black hole information paradox may be interpreted through similar templates.

Theoretical and Practical Implications

Theoretical insights derived from Maxwell’s demon and information theory deeply influence the understanding of quantum boundaries and classical thermodynamic laws. Practically, these interpretations hint at refining quantum computational models where control over quantum informational entropy is crucial.

1. Quantum Computation:

Exploring the thermodynamic costs of quantum information processing may shape future quantum computing designs, particularly those leveraging qubits’ thermal properties.

2. Information Theory Extensions:

By extending classical paradigms into quantum domains, the foundational aspects of computation and entropy are enriched, offering potential breakthroughs in how information is conceptually treated within physical systems.

3. Thermodynamic Systems Design:

The duel nature of information, both as a data construct and a physical entity incurring a cost, might influence future system designs across various scientific and engineering disciplines.

Concluding Remarks

The paper argues convincingly that the cross-pollination between physics and information theories harbors significant potential for unraveling complex phenomena in both classical and quantum domains. This paper frames Maxwell's demon not only as a historical curiosity but as a pivotal component in the broader narrative of entropy, computational laws, and quantum information systems. Future work could elaborate on these connections to foster more tangible applications in physics and engineering.