Computational Complexity Bounds for Maxwell's Demon: From Landauer's Principle to Quantum Advantage

Computational Complexity Bounds for Maxwell's Demon: From Landauer's Principle to Quantum Advantage | Research Square window.SnipcartSettings = { analytics: { enabled: false } }; (function() { var accessVector = localStorage.getItem('access_vector') || ''; window.dataLayer = window.dataLayer || []; if (accessVector) { window.dataLayer.push({ user: { profile: { profileInfo: { snid: accessVector } } } }); } })(); (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start':new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0],j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src='https://www.googletagmanager.com/gtm.js?id='+i+dl;f.parentNode.insertBefore(j,f);})(window,document,'script','dataLayer','GTM-K279D39R'); Browse Preprints In Review Journals COVID-19 Preprints AJE Video Bytes Research Tools Research Promotion AJE Professional Editing AJE Rubriq About Preprint Platform In Review Editorial Policies Our Team Advisory Board Help Center Sign In Submit a Preprint Cite Share Download PDF Research Article Computational Complexity Bounds for Maxwell's Demon: From Landauer's Principle to Quantum Advantage Rolando Pablo Hong Enriquez This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-8271063/v1 This work is licensed under a CC BY 4.0 License Status: Posted Version 1 posted You are reading this latest preprint version Abstract Whether quantum computational speedups translate to fundamental thermodynamic energy savings remains unresolved. We establish the first rigorous connection between computational complexity and thermodynamic costs through DEMON(I,E) complexity classes that classify information-processing protocols by information complexity I(n) and erasure energy E(n). Four theorems prove: (1) any g-bit erasure dissipates >= g X k_B T ln 2, generalizing Landauer's principle; (2) measurement disturbance D reduces extractable work to (I-D)k_B T ln 2; (3) Grover-based quantum demons achieve provably optimal Theta(sqrt{N}) thermodynamic advantage over classical search, tight by the BBBV lower bound; and (4) quantum walks on d-dimensional lattices exhibit a dense hierarchy with continuous scaling exponent (d-1)/(2d). Computational validation across six orders of magnitude confirms predictions with <1% error. Experimental predictions include 20.5X energy reduction for trapped-ion Grover search (N=1024, T=1 mK) and 11X effective cooling for superconducting circuit QED heat-bath protocols. This work unifies 158 years of Maxwell demon research, connects algorithmic complexity to physical energy costs, and enables experimental verification of quantum thermodynamic advantages beyond computational speedup. quantum thermodynamics Landauer erasure thermodynamic cost of computation Maxwell's demon Full Text Additional Declarations The authors declare no competing interests. Supplementary Files demonsupplementary.pdf Supplementary Information demonvalidationcode.zip Validation code (python) Cite Share Download PDF Status: Posted Version 1 posted You are reading this latest preprint version Research Square lets you share your work early, gain feedback from the community, and start making changes to your manuscript prior to peer review in a journal. As a division of Research Square Company, we’re committed to making research communication faster, fairer, and more useful. We do this by developing innovative software and high quality services for the global research community. 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We establish the first rigorous connection between computational complexity and thermodynamic costs through DEMON(I,E) complexity classes that classify information-processing protocols by information complexity I(n) and erasure energy E(n). Four theorems prove: (1) any g-bit erasure dissipates \u0026gt;= g X k_B T \u0026nbsp;ln 2, generalizing Landauer's principle; (2) measurement disturbance D reduces extractable work to (I-D)k_B T ln 2; (3) Grover-based quantum demons achieve provably optimal Theta(sqrt{N}) thermodynamic advantage over classical search, tight by the BBBV lower bound; and (4) quantum walks on d-dimensional lattices exhibit a dense hierarchy with continuous scaling exponent (d-1)/(2d). Computational validation across six orders of magnitude confirms predictions with \u0026lt;1% error. Experimental predictions include 20.5X energy reduction for trapped-ion Grover search (N=1024, T=1 mK) and 11X effective cooling for superconducting circuit QED heat-bath protocols. 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