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href="https://quantumquia.com/" rel="home">Quantum Quia</a></h1> <h2 class="site-description">state contenti, umana gente, al quia</h2> </div> </header> <div id="content" class="site-content"> <div id="primary" class="content-area"> <main id="main" class="site-main" role="main"> <article id="post-792" class="post-792 post type-post status-publish format-standard hentry category-research tag-entropy tag-philosophy tag-physics tag-science tag-thermodynamics"> <header class="entry-header"> <div class="entry-category"> <span class="cat-links"><a href="https://quantumquia.com/category/research/" rel="category tag">research</a></span> </div> <h1 class="entry-title">Maxwell’s demon, quantum theory, and the second law: who’s really in charge?</h1> <div class="entry-meta small-part"> <span class="posted-on"><i class="fa fa-clock-o space-left-right"></i><a href="https://quantumquia.com/2025/02/07/maxwells-demon-quantum-theory-and-the-second-law-whos-really-in-charge/" rel="bookmark"><time class="entry-date published" datetime="2025-02-07T19:27:18+09:00">February 7, 2025</time><time class="updated" datetime="2025-02-07T20:06:34+09:00">February 7, 2025</time></a></span><span class="byline"> <i class="fa fa-user space-left-right"></i><span class="author vcard"><a class="url fn n" href="https://quantumquia.com/author/buscemif/">francesco</a></span></span><span class="comments-link"><i class="fa fa-comments-o space-left-right"></i><a href="https://quantumquia.com/2025/02/07/maxwells-demon-quantum-theory-and-the-second-law-whos-really-in-charge/#respond">Leave a comment</a></span> </div> </header> <div class="entry-content"> <p>It is often said that the paradox of “Maxwell’s demon” is resolved by including the thermodynamic costs of measurement and memory erasure. The common claim is that these costs offset the demon’s apparent violation of the second law of thermodynamics, thereby restoring its validity. <strong>The truth, however, is quite the opposite</strong>: the fact that the costs of measurement and erasure offset the demon’s violation is a <em>consequence</em> of assuming that the second law is valid in the first place. In other words, it is the assumption of the validity of the second law that forces this equilibrium, not the other way around!</p> <p>This realization, which echoes the thesis of <a href="https://en.wikipedia.org/wiki/Maxwell%27s_demon">Earman and Norton</a>, came while studying some not-so-recent-anymore but still quite influential papers on quantum feedback protocols in quantum thermodynamics. While the narrative there adhered to the usual folklore on the subject (i.e., that quantum feedback protocols obey the second law whenever the thermodynamic costs of measurement and erasure are properly accounted for), what we found instead was quite different: quantum theory is in fact completely independent of the second law of thermodynamics! And it couldn’t be otherwise, simply because quantum theory has no built-in thermodynamics. <strong>There is no “quantum bullet” to exorcise Maxwell’s demon.</strong> In fact, in our work we explicitly constructed a model of a measurement and feedback process that violates the bounds required by the second law, even after including all costs (i.e., measurement and erasure costs) in the thermodynamic balance.</p> <p>However, we also found that <strong>although quantum theory can violate the second law, it does not need to</strong>: any quantum process can be realized in a way that does not violate the second law of thermodynamics, simply by adding more systems (bath, battery, and so on) until the thermodynamic balance is restored.</p> <p>There are two main takeaways from this story. First, even in quantum theory, it is the second law that guarantees the balance between gains and costs in feedback protocols, not the other way around. Second, although quantum theory and the second law of thermodynamics are logically independent, they can peacefully coexist. <strong>The second law of thermodynamics does not impose any hard constraints on what can be achieved in quantum theory</strong>: there is always a way to ensure compliance with the second law.</p> <p>In conclusion, by no means can we claim that quantum theory is “demon-proof” by design. However, we now have a much clearer understanding of how quantum feedback protocols work, what they can and cannot do. The paper appeared today on <a href="https://rdcu.be/d8Yxa">npj Quantum Information</a> but I like the look of the <a href="https://arxiv.org/abs/2308.15558">arXiv version</a> better.</p> <figure class="wp-block-image size-large"><a href="https://quantumquia.com/wp-content/uploads/2025/01/demon-in-quantum.webp"><img data-attachment-id="822" data-permalink="https://quantumquia.com/2025/02/07/maxwells-demon-quantum-theory-and-the-second-law-whos-really-in-charge/demon-in-quantum/" data-orig-file="https://quantumquia.com/wp-content/uploads/2025/01/demon-in-quantum.webp" data-orig-size="1024,1024" data-comments-opened="1" data-image-meta="{"aperture":"0","credit":"","camera":"","caption":"","created_timestamp":"0","copyright":"","focal_length":"0","iso":"0","shutter_speed":"0","title":"","orientation":"0"}" data-image-title="demon-in-quantum" data-image-description="" data-image-caption="" data-medium-file="https://quantumquia.com/wp-content/uploads/2025/01/demon-in-quantum.webp?w=300" data-large-file="https://quantumquia.com/wp-content/uploads/2025/01/demon-in-quantum.webp?w=809" width="1024" height="1024" src="https://quantumquia.com/wp-content/uploads/2025/01/demon-in-quantum.webp?w=1024" alt="" class="wp-image-822" /></a><figcaption class="wp-element-caption">Quantum theory can exorcise Laplace’s demon. But Maxwell’s demon is still lurking…</figcaption></figure> <p></p> <div id="jp-post-flair" class="sharedaddy sd-like-enabled sd-sharing-enabled"><div class="sharedaddy sd-sharing-enabled"><div class="robots-nocontent sd-block sd-social sd-social-icon-text sd-sharing"><h3 class="sd-title">Share this:</h3><div class="sd-content"><ul><li class="share-twitter"><a rel="nofollow noopener noreferrer" data-shared="sharing-twitter-792" class="share-twitter sd-button share-icon" href="https://quantumquia.com/2025/02/07/maxwells-demon-quantum-theory-and-the-second-law-whos-really-in-charge/?share=twitter" target="_blank" title="Click to share on Twitter" ><span>Twitter</span></a></li><li class="share-facebook"><a rel="nofollow noopener noreferrer" data-shared="sharing-facebook-792" class="share-facebook sd-button share-icon" href="https://quantumquia.com/2025/02/07/maxwells-demon-quantum-theory-and-the-second-law-whos-really-in-charge/?share=facebook" target="_blank" title="Click to share on 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Our results show that this assumption leads to a fundamental […]'>The thermodynamic trilemma of efficient measurements</a></li><li><a class='rsswidget' href='http://arxiv.org/abs/1910.04294v3' title='The Alberti-Uhlmann criterion states that any given qubit dichotomy can be transformed into any other given qubit dichotomy by a quantum channel if and only if the testing region of the former dichotomy includes the testing region of the latter dichotomy. Here, we generalize the Alberti-Uhlmann criterion to the case of arbitrary number of qubit or qutrit sta […]'>Extension of the Alberti-Uhlmann criterion beyond qubit dichotomies</a></li><li><a class='rsswidget' href='http://arxiv.org/abs/2501.16878v1' title='Telecloning is a protocol introduced by Murao et al. to distribute copies of an unknown quantum state to many receivers in a way that beats the trivial ``clone-and-teleport'' protocol. 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Most studies to date have focused on fine-tuned catalytic processes that are highly sensiti […]'>Robust Catalysis and Resource Broadcasting: The Possible and the Impossible</a></li><li><a class='rsswidget' href='http://arxiv.org/abs/2404.11985v2' title='Observational entropy -- a quantity that unifies Boltzmann's entropy, Gibbs' entropy, von Neumann's macroscopic entropy, and the diagonal entropy -- has recently been argued to play a key role in a modern formulation of statistical mechanics. Here, relying on algebraic techniques taken from Petz's theory of statistical sufficiency and on […]'>On the generic increase of observational entropy in isolated systems</a></li><li><a class='rsswidget' href='http://arxiv.org/abs/2308.15558v3' title='Adiabatic measurements, followed by feedback and erasure protocols, have often been considered as a model to embody Maxwell's Demon paradox and to study the interplay between thermodynamics and information processing. 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