The standard Landauer bound W≥kBTln2 sets the fundamental thermodynamic cost for information erasure under ideal conditions: weak system–bath coupling, quasistatic operation, and equilibrium reservoirs. However, realistic quantum error correction (QEC) operates in a profoundly different regime—finite-time syndrome extraction, strong coupling to cryogenic environments, and non-equilibrium dynamics. Here, we develop a unified thermodynamic framework for fault-tolerant quantum computing that incorporates corrections beyond the ideal Landauer limit. We derive a generalized bound on the heat dissipation per QEC cycle: Qmin≥kBTln2+kBTΔISB+ℏτ, and scaling this result to large-scale quantum computers, we find that the total heat load grows polynomially with code distance but remains in the nanowatt range for million-qubit systems—well within the cooling power of modern dilution refrigerators. Applying our model to superconducting qubit architectures, we show that while strong coupling can add up to ∼20% to the ideal cost, finite-time effects contribute approximately 0.55% at 100 ns and 5.5% at 10 ns reset operations. Our results establish that the true thermodynamic cost of fault tolerance, while exceeding the naive Landauer estimate, does not pose a fundamental obstacle to scalability; the dominant engineering challenges lie in the heat load of control electronics and wiring, not in the fundamental dissipation of qubit reset.

In this work we present a hierarchy of generalized contextuality. It refines the traditional binary distinction between contextual and noncontextual theories, and facilitates their comparison based on how contextual they are. Our approach focuses on the contextuality of prepare-and-measure scenarios, described by general probabilistic theories (GPTs). To motivate the hierarchy, we define it as the resource ordering of a novel resource theory of GPT-contextuality. The building blocks of its free operations are classical systems and univalent simulations between GPTs. These simulations preserve operational equivalences and thus cannot generate contextuality. Noncontextual theories can be recovered as least elements in the hierarchy. We then define a new contextuality monotone, called classical excess, given by the minimal error of embedding a GPT within an infinite classical system. In addition, we show that the optimal success probability in the parity oblivious multiplexing game also defines a monotone in our resource theory. Finally, we discuss whether the non-free operations can be understood as implementing information erasure and thus explaining the fine-tuning aspect of contextuality.

We measured the energy efficiency of information erasure using silicon DRAM cells capable of counting charges on capacitors at the single-electron level. Our measurements revealed that the efficiency decreased as the erasure error probability decreased, and notably, the Landauer limit was not achieved, even under effectively infinite-time bit erasure. By comparing the measured efficiency with the Landauer limit, we identified a thermodynamic constraint that prevents DRAM from reaching this limit: the inability to prepare the initial state in thermal equilibrium, which in turn, prohibits quasistatic operations. This finding has broad implications for DRAM cells and for many electronic circuits sharing similar structures. Furthermore, it validates our experimental approach to discovering thermodynamic constraints that impose tighter, practically relevant limits, opening a new direction in information thermodynamics research.

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.

The measurement problem in quantum mechanics challenges our understanding of reality, demanding explanations beyond both Copenhagen's "collapse" and the Many-Worlds' ontological multiplicity. This paper introduces and formalizes the Ze framework as a novel synthesis of Relational Quantum Mechanics (RQM) and the Active Inference paradigm from theoretical neuroscience. Ze posits that quantum states are relational, defined by the posterior beliefs of interacting generative models engaged in variational free energy minimization. Within this framework, quantum superposition is formalized as high compatibility (ℐ ≈ 1) between competing models, characterized by low free-energy conflict (ΔF < θ). Conversely, the transition to a localized state—the physical correlate of "collapse"—is reconceived not as a metaphysical event but as an optimization-driven phase transition. This occurs when model conflict exceeds a critical threshold (ΔF > θ), a process objectively driven by interactions like which-path marking. We demonstrate that matter-wave interferometry with complex molecules provides a direct experimental testbed for these principles, where which-path information and quantum erasure actively manipulate ΔF. Extending the isomorphism, we propose that transitions in human cognition—from focused wakefulness to dreaming and psychedelic states—are governed by analogous shifts in the brain's inferential threshold (θ). Thus, Ze offers a unified, testable architecture bridging quantum foundations, statistical physics, and the neuroscience of consciousness.

Whether a photon exhibits wavelike or particlelike behavior depends on the observation method, as clearly demonstrated by the quantum erasure (QE) experiments. Here, we propose a novel, to the best of our knowledge, version of the QE experiment that leverages a single photon prepared in an arbitrary polarization superposition state. Unlike traditional approaches that have a definite erasure method, the erasure in our experiment is determined intrinsically by the photon's quantum state at the moment of measurement. Furthermore, we observe continuous morphing between wave and particle behavior, enabled by continuous path information erasure in the photon's transverse mode. This dynamic transition challenges the classical dichotomy of waves and particles. These findings provide deeper insight into Bohr's complementarity principle and expand the conceptual framework of quantum mechanics.

Utilizing DNA's molecular programmability, massive parallelism, and minimal energy requirements, it emerges as a transformative medium for secure data storage and encryption. However, practical implementation is limited by technical challenges, particularly the development of robust, programmable systems for flexible data encoding, precise molecular operations, and reliable encryption. Here, we present a molecular information storage and encryption platform that integrates hierarchical core-shell DNA condensates with biomolecular computing networks. It allows programmable and rapid execution of core operations such as information encoding, erasure, rewriting, replication, and repair within readily accessible and readable DNA-based condensates. Moreover, programmable biomolecular computing circuits endowed the system with unprecedented encryption capabilities, including multi-level logic encryption, time-dependent dynamic encryption, living system-driven encryption and fine-grained access control of information. Together, this work represents a meaningful advancement in molecular information storage and encryption, with notable advantages in dynamic editability and system scalability.

Optimal transport theory, originally developed in the 18th century for civil engineering, has since become a powerful optimization framework across disciplines, from generative AI to cell biology. In physics, it has recently been shown to set fundamental bounds on thermodynamic dissipation in finite-time processes. This extends beyond the conventional second law, which guarantees zero dissipation only in the quasi-static limit and cannot characterize the inevitable dissipation in finite-time processes. Here, we experimentally realize thermodynamically optimal transport using optically trapped microparticles, achieving minimal dissipation within a finite time. As an application to information processing, we implement the optimal finite-time protocol for information erasure, confirming that the excess dissipation beyond the Landauer bound is exactly determined by the Wasserstein distance — a fundamental geometric quantity in optimal transport theory. Furthermore, our experiment achieves the bound governing the trade-off between speed, dissipation, and accuracy in information erasure. To enable precise control of microparticles, we develop scanning optical tweezers capable of generating arbitrary potential profiles. These results provide guiding principles for information processing with saturating the trade-off.

Landauer’s principle provides a deep connection between information processing and thermodynamics by setting a lower limit on the energy consumption and heat production of logically irreversible transformations. However, Landauer’s original formulation assumes that information is initially stored in an equilibrium state, whereas real devices often operate with out-of-equilibrium states. Here, we experimentally demonstrate that nonequilibrium memory states can provide a useful resource for fast information erasure below the equilibrium bounds by using an underdamped levitated optomechanical system. To that end, we introduce a versatile optical levitation scheme that enables fast and precise dynamical shaping of general potential landscapes. By harnessing the energy and entropy of an initial nonequilibrium two-state memory, we demonstrate reduced power consumption as well as negative heat production during erasure. Our findings significantly broaden the range of tools available in levitodynamics and suggest that the engineering of appropriate far-from-equilibrium memory states could pave the way for an approach to heat management.

Elucidating fundamental limitations inherent in physical systems is a central subject in physics. For important thermodynamic operations such as information erasure, cooling, and copying, resources like time and energetic cost must be expended to achieve the desired outcome within a predetermined error margin. In the context of cooling, the unattainability principle of the third law of thermodynamics asserts that infinite “resources” are needed to reach absolute zero. However, the precise identification of relevant resources and how they jointly constrain achievable error remains unclear within the frameworks of stochastic and quantum thermodynamics. In this work, we introduce the concept of separated states, which consist of fully unoccupied and occupied states, and formulate the corresponding thermokinetic cost and error, thereby establishing a unifying framework for a broad class of thermodynamic operations. We then uncover a three-way trade-off relation between time, cost, and error for thermodynamic operations aimed at creating separated states, simply expressed as τ C ϵ τ ≥ 1 − η . This fundamental relation is applicable to diverse thermodynamic operations, including information erasure, cooling, and copying. It provides a profound quantification of the unattainability principle in the third law of thermodynamics in a general form. Building upon this relation, we explore the quantitative limitations governing cooling operations, the preparation of separated states, and a no-go theorem for exact classical copying. Furthermore, we extend these findings to the quantum regime, encompassing both Markovian and non-Markovian dynamics. Specifically, within Lindblad dynamics, we derive a similar three-way trade-off relation that quantifies the cost of achieving a pure state with a given error. The generalization to general quantum dynamics involving a system coupled to a finite bath implies that the dissipative cost becomes infinite as the quantum system is exactly cooled down to the ground state or perfectly reset to a pure state, thereby resolving an open question regarding the thermodynamic cost of information erasure.

Quantum-foundational implications of information erasure upon measurement

Information engines, sometimes referred to as Maxwell Demon engines, utilize information obtained through measurement to control the conversion of energy into useful work. Discussions around such devices often assume the measurement step to be instantaneous, assessing its cost by Landauer's information erasure within the measurement device. While this simplified perspective is sufficient for classical feedback-controlled engines, for nanoengines that often operate in the quantum realm, the overall performance may be significantly affected by the measurement duration (which may be comparable to the engine's cycle time) and cost (energy needed to create the system-meter correlation). In this study, we employ a generalized von Neumann measurement model to highlight that obtaining a finite amount of information requires a finite measurement time and incurs an energetic cost. We investigate the crucial role of these factors in determining the engine's performance, particularly in terms of efficiency and power output. Furthermore, for the information engine model under consideration, we establish a precise relationship between the acquired information in the measurement process and the maximum energy extractable through the measurement. We also discuss ways to extend our considerations using these concepts, such as in measurement-enhanced photochemical reactions.

Abstract Recent experiments have implemented resetting by means of a time-varying external harmonic trap, whereby the trap stiffness is changed in finite-time and the system is reset when it relaxes to an equilibrium distribution in the final trap. Such setups are very similar to those studied in the context of the finite-time Landauer erasure principle. In this work, we analyze the thermodynamic costs of such a setup by deriving a moment generating function for the work cost of recurrently changing the trap stiffness, thereby maintaining a non-equilibrium steady state. For this heretofore unstudied case, we obtain explicit expressions for the mean and variance of the work both for a specific experimentally viable protocol as well as an optimal protocol which minimizes the mean cost. For both these procedures, our analysis captures both the large-time and short-time corrections. For the optimal protocol, we obtain a closed form expression for the mean cost for all protocol durations, thereby making contact with earlier work on geometric measures of dissipation-minimizing optimal protocols that implement information erasure.

We introduce a numerical method to sample the distributions of charge, heat, and entropy production in open quantum systems coupled strongly to macroscopic reservoirs, with both temporal and energy resolution and beyond the linear-response regime. Our method exploits the mesoscopic-leads formulation, where macroscopic reservoirs are modeled by a finite collection of modes that are continuously damped toward thermal equilibrium by an appropriate Gorini-Kossakowski-Sudarshan-Lindblad master equation. Focussing on noninteracting fermionic systems, we access the time-resolved full counting statistics through a trajectory unraveling of the master equation. We show that the integral fluctuation theorems for the total entropy production, as well as the martingale and uncertainty entropy production, hold. Furthermore, we investigate the fluctuations of the dissipated heat in finite-time information erasure. Conceptually, our approach extends the continuous-time trajectory description of quantum stochastic thermodynamics beyond the regime of weak system-environment coupling.

Large deviation theory (LDT) provides a mathematical framework to quantify the probabilities of rare events in stochastic systems. In this study, we applied LDT to model a chemical reaction system and demonstrated that the fluctuation theorem for nonequilibrium reaction systems can be derived from the symmetry of the cumulant generating function defined through the rate function. Notably, this derivation does not depend on the assumption of local detailed balance. Furthermore, we redefined heat using this rate function based on information theory and evaluated Landauer's principle, which addresses the minimum energy cost associated with information erasure. These findings show the utility of LDT as a comprehensive framework for analyzing a wide range of nonequilibrium systems.

I dispute the conventional claim that the second law of thermodynamics is saved from a “Maxwell’s demon” by the entropy cost of information erasure and show that instead it is measurement that incurs the entropy cost. Thus, Brillouin, who identified measurement as savior of the second law, was essentially correct, and putative refutations of his view, such as Bennett’s claim to measure without entropy cost, are seen to fail when the applicable physics is taken into account. I argue that the tradition of attributing the defeat of Maxwell’s demon to erasure rather than to measurement arose from unphysical classical idealizations that do not hold for real gas molecules, as well as a physically ungrounded recasting of physical thermodynamical processes into computational and information-theoretic conceptualizations. I argue that the fundamental principle that saves the second law is the quantum uncertainty principle applying to the need to localize physical states to precise values of observables in order to effect the desired disequilibria aimed at violating the second law. I obtain the specific entropy cost for localizing a molecule in the Szilard engine and show that it coincides with the quantity attributed to Landauer’s principle. I also note that an experiment characterized as upholding an entropy cost of erasure in a “quantum Maxwell’s demon” actually demonstrates an entropy cost of measurement.

Abstract We report on the preparation of a large quantum register of 5612 qubits, with the unprecedented high global fidelity of F ≃ 0.9956 . This was achieved by applying an improved cooperative quantum information erasure protocol (Buffoni and Campisi 2023 Quantum 7 961) to a programmable network of superconducting qubits featuring a high connectivity. At variance with the standard method based on the individual reset of each qubit in parallel, here the quantum register is treated as a whole, thus avoiding the well-known orthogonality catastrophe whereby even an extremely high individual reset fidelity f results in vanishing global fidelities F = f N with growing number N of qubits.

I dispute the conventional claim that the second law of thermodynamics is saved from a "Maxwell's Demon" by the entropy cost of information erasure, and show that instead it is measurement that incurs the entropy cost. Thus Brillouin, who identified measurement as savior of the second law, was essentially correct, and putative refutations of his view, such as Bennett's claim to measure without entropy cost, are seen to fail when the applicable physics is taken into account. I argue that the tradition of attributing the defeat of Maxwell's Demon to erasure rather than to measurement arose from unphysical classical idealizations that do not hold for real gas molecules, as well as a physically ungrounded recasting of physical thermodynamical processes into computational and information-theoretic conceptualizations. I argue that the fundamental principle that saves the second law is the quantum uncertainty principle applying to the need to localize physical states to precise values of observables in order to effect the desired disequilibria aimed at violating the second law. I obtain the specific entropy cost for localizing a molecule in the Szilard engine, which coincides with the quantity attributed to Landauer's principle. I also note that an experiment characterized as upholding an entropy cost of erasure in a "quantum Maxwell's Demon" actually demonstrates an entropy cost of measurement.

Quantum complexity measures the difficulty of realizing a quantum process, such as preparing a state or implementing a unitary. We present an approach to quantifying the thermodynamic resources required to implement a process if the process’s complexity is restricted. We focus on the prototypical task of information erasure, or Landauer erasure, wherein an n-qubit memory is reset to the all-zero state. We show that the minimum thermodynamic work required to reset an arbitrary state in our model, via a complexity-constrained process, is quantified by the state’s . The complexity entropy therefore quantifies a trade-off between the work cost and complexity cost of resetting a state. If the qubits have a nontrivial (but product) Hamiltonian, the optimal work cost is determined by the . The complexity entropy quantifies the amount of randomness a system appears to have to a computationally limited observer. Similarly, the complexity relative entropy quantifies such an observer’s ability to distinguish two states. We prove elementary properties of the complexity (relative) entropy. In a random circuit—a simple model for quantum chaotic dynamics—the complexity entropy transitions from zero to its maximal value around the time corresponding to the observer’s computational-power limit. Also, we identify information-theoretic applications of the complexity entropy. The complexity entropy quantifies the resources required for data compression if the compression algorithm must use a restricted number of gates. We further introduce a , which arises naturally in a complexity-constrained variant of information-theoretic decoupling. Assuming that this entropy obeys a conjectured chain rule, we show that the entropy bounds the number of qubits that one can decouple from a reference system, as judged by a computationally bounded referee. Overall, our framework extends the resource-theoretic approach to thermodynamics to integrate a notion of , as quantified by .

Landauer's limit on heat dissipation during information erasure is critical as devices shrink, requiring optimal pure-state preparation to minimize errors. However, Nernst's third law states this demands infinite resources in energy, time, or control complexity. We address the challenge of cooling quantum systems with finite resources. Using Markovian collision models, we explore resource trade-offs and present efficient cooling protocols (that are optimal for qubits) for coherent and incoherent control. Leveraging thermodynamic length, we derive bounds on heat dissipation for swap-based strategies and discuss the limitations of preparing pure states efficiently.