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.
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.
Abstract Computation requires energy. Landauer’s principle establishes that erasing one bit of information irreversibly dissipates at least kBT ln 2 of thermal energy. Modern computers operate 10^6 to 10^9 times above this fundamental bound. In 1973, Bennett demonstrated that any computation can be made thermodynamically reversible through procedures that preserve information, thereby approaching the Landauer limit. However, a critical question remained unanswered for fifty years: how quickly does reversible compilation converge to the theoretical minimum, and what ensemble size achieves practical energy savings? We resolve this problem through the Fluctuation-Dissipation Compilation Theorem, which provides the first explicit convergence rate for thermodynamically optimal computing. Reversible compilation of any algorithm dissipates average energy equal to the thermal energy scale multiplied by the logical entropy change, plus corrections that decrease as the inverse square root of the ensemble size. This N^(−1/2) convergence rate, derived by combining fluctuation theorems from statistical mechanics with the central limit theorem, is provably optimal—no compilation strategy can achieve faster convergence. The proof unifies three historically independent disciplines: statistical mechanics through the Jarzynski equality and Crooks fluctuation theorem, information theory through Shannon entropy bounds, and compilation theory through Bennett’s reversible computing framework. By formulating thermodynamic compilation as a rigorous resource theory, we establish that reversible transformations exactly conserve entropy while irreversible erasure operations incur fundamental energy costs bounded by information-theoretic limits. Critically, we provide finite-ensemble performance guarantees essential for practical implementations, characterizing not just average energy dissipation but complete statistical distributions including fluctuations and tail probabilities. Numerical experiments on Grover search and quantum Fourier transforms validate our predictions. Simulations confirm the predicted N^(−1/2) convergence rate within 3% error and demonstrate energy reductions exceeding 99.9% compared to irreversible implementations. These results establish that thermodynamically optimal compilation is achievable with realistic ensemble sizes for near-term quantum hardware operating under thermal constraints. This framework bridges fundamental physics and practical computing. Applications span quantum processors cooled to millikelvin temperatures where every picojoule of dissipation limits performance, battery-powered Internet-of-Things sensors requiring decade-long autonomous operation, data centers consuming one percent of global electricity where incremental efficiency improvements yield billion-dollar savings, and deep-space missions operating on hundred-watt radioisotope generators where every watt conserved enables additional science. By establishing thermodynamic compilation as a rigorous engineering discipline with explicit finite-size guarantees, this work transforms Bennett’s asymptotic theoretical insight into a practical methodology for approaching fundamental physical limits in real computing systems
We conducted a comprehensive numerical simulation study on the practical limitations of information engines (energy harvesters) based on Maxwell's Demon, as well as on the quantum information thermodynamic breakthroughs that overcome these limitations. First, using a rigorous master equation simulation (Partial-Secular Semilocal Lindblad approach) of an autonomous engine employing quantum dots, we identified its fatal vulnerabilities (breakdown thresholds) to heat leakage and measurement errors. Furthermore, as a scalable architecture to overcome these limitations, we proposed an "Information Conveyor Belt based on continuous measurement and Bayesian inference" using superconducting circuits, and demonstrated powerful work extraction against a massive reverse bias in a 10-dot chain. Finally, challenging the prohibition of perpetual motion machines dictated by the classical Landauer's principle (information erasure cost), we proved the phenomenon of "negative erasure cost (Quantum Landauer Loophole)" using maximum quantum entanglement via simulations, thereby demonstrating the physical feasibility of true second-kind perpetual motion operation (pure power generation by spontaneous thermal excitation) at room temperature.
Irreversibility has a fundamental thermodynamic cost, erasing information inevitably generates heat. This connection is quantified by the Landauer bound, which gives the minimum dissipation needed to erase a single bit of information. While this bound applies in both classical and quantum settings, it is saturated only in idealised limits of infinite resources. Here, we provide a unified first principles description of finite-resource erasure in both classical and quantum systems. We begin by proving the communal folklore that in the idealised regime the erasure cost of a bit encoded in a quantum or classical system is the same. Despite this, we show that their practical implementation differs substantially: achieving comparable erasure quality in quantum systems requires more control, larger accessible energy gaps and longer operation times. Classical protocols can achieve the erasure of a comparable quantum protocol under far weaker constraints which we expose in trade-off relations. Our results explain why practical erasure schemes fall short of Landauer's bound and show that classical systems enjoy several fundamental thermodynamic advantages.
We present a unified theoretical, numerical, and experimental investigation into autonomous information heatengines (Maxwell’s demons), bridging microscopic open quantum thermodynamics, stochastic continuous moni-toring, deep reinforcement learning, and practical energy harvesting engineering. First, addressing widespreadnumerical pitfalls in quantum thermodynamics simulations, we identify an operator sign inversion in detailed-balance jump rates that previously simulated an unphysical “perpetual motion machine” yielding −19.29 kB T .Once corrected via adaptive Runge-Kutta integration, we prove that single-step work extraction from maximallyentangled Bell states is strictly bounded by kB T ln 2, and that the cyclic entropy accounting of entanglement re-generation imposes a net non-negative work cost (Wnet ≥ 0), establishing quantum entanglement as a consumedthermodynamic fuel rather than a violation of the Second Law. Second, using positive-preserving Rouchon-Ralphstochastic master equation mappings across 48 trajectory ensembles, we evaluate an Information Conveyor Beltin a 10-dot chain under continuous homodyne detection. We demonstrate that while an isolated cryogenic demonreservoir (TM = 4.2 K) enables positive extracted power, incorporating the mandatory Carnot refrigeration over-head required to maintain the cryostat exactly cancels all efficiency advantages, yielding an overall system deficitmatching the isothermal baseline. Third, we address autonomous control in partially observable Markov deci-sion processes (POMDPs) by deploying Recurrent Proximal Policy Optimization (Recurrent PPO with LSTM),enabling the demon to autonomously overcome measurement backaction and discover synchronized conveyor trans-port policies superior to classical heuristics. Finally, we design and verify Configuration D, a body-heat-poweredthermoelectric energy harvester operating an ESP32-C3 microcontroller demon. By eliminating idle wake-timedelays and overlapping 9-bit digital sensor conversion with sub-millisecond USB polling, firmware v2 slashes ac-tive controller consumption in our calibrated design model by a factor of 8.7 (from ≈ 208.5 mJ to ≈ 24.1 mJ),establishing a net-positive self-powered operational cycle (+65.8 mJ/cycle). We quantify the fundamental gap of≈ 8.4 × 1018 (≈ 19 orders of magnitude) between the Landauer erasure limit (2.87 × 10−21 J) and real-worldmicrocontrollers, delineating the rigorous boundary between physical information thermodynamics and real-worldenergy harvesting.
The Landauer's principle, a cornerstone of information thermodynamics, provides a fundamental lower bound on the energetic cost of information erasure in terms of the information content change. However, its traditional formulation is largely confined to systems exchanging solely energy with an ideal thermal bath. In this work, we derive general information-cost trade-off relations that go beyond the scope of Landauer's principle by developing a thermodynamic inference approach based on the maximum entropy principle. These relations require only information about the system and are applicable to complex quantum scenarios involving multiple conserved charges and non-thermal environments. Specifically, we present two key results: (i) In scenarios where only the mean values of observables are accessible, we derive an information-content-informed upper bound on the thermodynamic cost which complements an existing generalized Landauer lower bound. (ii) When second-order fluctuations can also be measured, we obtain an information-content-informed lower bound on the change in variances of observables, thereby extending the Landauer's principle to constrain higher-order fluctuation costs. We numerically validate our information-cost trade-off relations using a coupled-qubit system exchanging energy and excitations, a driven qubit implementing an information erasure process, and a driven double quantum dot system that can operate as an inelastic heat engine. Our results underscore the broad utility of maximum-entropy inference in constraining thermodynamic costs for generic finite-time quantum processes, with direct relevance to quantum information processing and quantum thermodynamic applications.