This research establishes an operational lower bound on entropy production induced by mass gaps in quantum systems. Using completely positive trace-preserving (CPTP) dynamics, the study demonstrates that any physical reset of a system with a minimal spectral gap \delta_{min}=mc^{2} incurs a minimum entropy production defined by the relation \Sigma\ge mc^{2}/T. Unlike Landauer's principle, this bound follows purely from thermodynamic admissibility and spectral structure rather than logical irreversibility or information-theoretic arguments. Key Features of the Study: ELQR Framework: The research utilizes the Entropy-Limited Quantum Reset (ELQR) framework to model reset as a constrained CPTP control problem. Reinforcement Learning Validation: Optimization using RL agents (specifically PPO) shows that the theoretical bound emerges as a robust dynamical attractor under unconstrained control optimization. Hawking Emission Application: When applied to black-hole horizons, the bound implies a minimal entropic cost for Hawking emission per particle of mass m that is independent of information loss or Page-curve considerations. Many-Body Systems: Validated through tensor-network simulations (TeNPy) of short Heisenberg chains, confirming that the operational bound is robust even in correlated systems. Non-Markovian Extensions: Preliminary simulations of qubits coupled to memory show that while transient backflow occurs, the envelope remains consistent with the mass-induced limit.
This research establishes an operational lower bound on entropy production induced by mass gaps in quantum systems. Using completely positive trace-preserving (CPTP) dynamics, the study demonstrates that any physical reset of a system with a minimal spectral gap \delta_{min}=mc^{2} incurs a minimum entropy production defined by the relation \Sigma\ge mc^{2}/T. Unlike Landauer's principle, this bound follows purely from thermodynamic admissibility and spectral structure rather than logical irreversibility or information-theoretic arguments. Key Features of the Study: ELQR Framework: The research utilizes the Entropy-Limited Quantum Reset (ELQR) framework to model reset as a constrained CPTP control problem. Reinforcement Learning Validation: Optimization using RL agents (specifically PPO) shows that the theoretical bound emerges as a robust dynamical attractor under unconstrained control optimization. Hawking Emission Application: When applied to black-hole horizons, the bound implies a minimal entropic cost for Hawking emission per particle of mass m that is independent of information loss or Page-curve considerations. Many-Body Systems: Validated through tensor-network simulations (TeNPy) of short Heisenberg chains, confirming that the operational bound is robust even in correlated systems. Non-Markovian Extensions: Preliminary simulations of qubits coupled to memory show that while transient backflow occurs, the envelope remains consistent with the mass-induced limit.
Quantum information reset is an intrinsically irreversible process constrained by the second law of thermodynamics. In contemporary superconducting processors, dissipation during qubit reset is frequently dominated not only by quantum limits but by a classical energy floor on the order of 10^{-21} J. In contrast, the entropic bound T \Delta S at dilution refrigerator temperatures (\sim 15 mK) corresponds to a lower energy scale of approximately 10^{-23} J, establishing entropy production as the organizing physical principle that limits both the efficiency and the speed of reset operations. We introduce an entropy-limited efficiency estimator, \eta_S = 1 - (T \Delta S / W_{\rm diss}), which quantifies the thermodynamic distance from the entropic (Landauer) limit. By construction, \eta_S = 0 corresponds to the saturation of the entropy production limit, while \eta_S \to 1 indicates dissipation dominated by non-entropic (classical) contributions. Maximizing \eta_S is equivalent to a constrained variational problem in which dissipated work is minimized subject to the second law of thermodynamics. For typical superconducting qubits (\omega_q/2\pi \sim 5 GHz, T_1 \sim 50–100 \mus, T \sim 15 mK), the entropic bound T \Delta S \sim 10^{-23} J lies two orders of magnitude below the experimentally observed classical dissipation floor W_{\rm floor} \sim 10^{-21} J. Figures 1 and 2 were generated using the provided scripts_generate_figures.py script, using parameters: \omega_q/2\pi = 5 GHz, T_1 = 80 \mus, and T = 15 mK.
The erasure of quantum information is governed by two fundamental thermodynamic bounds: Landauer’s principle, which establishes the absolute minimum energetic cost of resetting a state, and Nernst’s unattainability principle, which dictates that perfect cooling to absolute zero entropy requires infinite resources. Under finite constraints, conventional cooling protocols utilizing thermal baths composed of n non-interacting particles are bottlenecked by a linear dissipation barrier (O(1/n)). In this thesis, we establish the ultimate thermodynamic limits of finite-resource multiqubit erasure and introduce the most thermodynamically efficient cooling protocol currently known. Building upon the max-cooling framework—a global unitary operation that systematically sorts the eigenvalues of the joint system-bath state to pack the highest probability mass into the target’s ground state—we engineer a bath Hamiltonian with specific, target-dependent degeneracies for arbitrary m-qubit systems. This collective protocol achieves an optimal asymptotic entropy production scaling of Σ = O(mˆ2/nˆ2), successfully saturating the scaling of the fundamental theoretical lower bound. This degeneracy-optimized approach strictly outperforms both standard non-interacting reservoirs and the best-known protocol for the independent cooling of single qubits using a reservoir of interacting particles (O(mˆ3/nˆ2)). Furthermore, we establish that surpassing conventional dissipation barriers requires an operational threshold of just n ≥ 2mˆ2 bath particles to achieve this optimal scaling.
This preprint examines the thermodynamic limits of information registration and their implications for quantum mechanics, black hole physics, and cosmology. Building on Landauer’s principle, it argues that registration and erasure are physically inseparable operations, each incurring the same energetic toll of kBTln2 per bit. From this perspective, quantum “collapse” is reframed as collapse insolvency, the condition that stable records cannot be formed beyond an energy constrained ceiling. The paper develops a Six Tier Insolvency Model, distinguishing between global constraints (Bekenstein–Hawking entropy, Landauer throughput, empirical ceilings) and local bottlenecks (Hawking flux, flux dilution, observer collapse limit). It derives striking insolvency ratios (~10⁻⁵⁶ globally and ~10⁻⁴⁷ locally), quantifying the gap between the entropy accessible in principle and that which any finite observer can render. The analysis introduces the Goldilocks Rendering Zone (GRZ), a universal band where collapse can occur: too little flux leaves no record, too much flux exceeds solvency. This provides a unified account that links quantum measurement, biological information processing, and black hole horizons under the same energetic constraint. The framework is falsifiable. It predicts a hard ceiling of ~10¹² bits·s⁻¹·m⁻² for sustained registration under standard conditions (300 K, 1 W/m²). A single reproducible counterexample would suffice to overturn the model.
In practice, qubit reset must be operated in an extremely short time, which incurs a thermodynamic cost within multiple orders of magnitude above the Landauer bound. We present a general framework to determine the minimal thermodynamic cost and the corresponding optimal protocol for memory erasure under arbitrary erasure speeds. Our study reveals the divergent behavior of minimal entropy production in the short-time limit depends on the convergence and divergence of the jump operator. There is an inherent trade-off between the minimal required time and the set error probability for the convergent class. Moreover, we find the optimal protocol exhibits general features in the fast-driving regime. To illustrate these findings, we employ fermionic and bosonic baths as examples. Our results suggest that the super-Ohmic bosonic heat bath is suitable for qubit reset.
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 .
Abstract The mass gap—defined as the minimum excitation energy above the ground state—represents one of the most fundamental quantities in quantum field theory and condensed matter physics. Its existence ensures spectral isolation of the ground state, exponential decay of spatial correlations, and determines the low-temperature thermodynamic behavior of quantum many-body systems. Despite its central importance, rigorous lower bounds on the mass gap that can be explicitly computed from microscopic parameters have remained elusive for realistic lattice models. This work presents a comprehensive examination of the Nemirovsky bound, a recently established mathematical inequality that provides an explicit lower limit for the mass gap in lattice quantum systems: Δ ≥ Λgate(g) = m₀ − 2zgVmax > 0, valid for coupling strengths g < g* = m₀/(2zVmax) Here m₀ denotes the local mass gap at a single lattice site, z is the coordination number encoding lattice topology, Vmax represents the maximum nearest-neighbor interaction amplitude, and g controls the coupling strength. The bound emerged as the culmination of a seven-part research program on the Spectral Vacuum Mechanism (SVM), progressing from phenomenological descriptions of elementary particle masses through rigorous constructive proofs on two-dimensional and three-dimensional lattices. We demonstrate how this fundamental quantum constraint directly determines macroscopic thermodynamic properties through its role in the partition function. At temperatures T ≪ Δ/k, the heat capacity exhibits characteristic activation behavior CV(T) ~ (Δ/kT)² exp(−Δ/kT), with the exponential suppression governed by the Nemirovsky bound. The entropy vanishes as S(T) → 0 when T → 0, ensuring compliance with the third law of thermodynamics. The critical coupling g* = m₀/(2zVmax) precisely demarcates the quantum phase transition at T = 0, where the gap closes and the system transitions from an insulating gapped phase to a conducting gapless phase with qualitatively different correlation structure. Three detailed numerical examples illustrate the practical application of the formula across diverse physical systems. For a quantum antiferromagnet on a cubic lattice (m₀ = 100 K, z = 6, Vmax = 10 K, g = 0.3), the bound predicts Δ ≥ 64 K, leading to exponential freezing of heat capacity below T ≈ 15 K. Near the critical point, the gap decreases linearly as Δ = m₀(1 − g/g*), vanishing at g = g* = 0.833. For topological quantum qubits with parameters m₀ = 1.0 meV and Vmax = 0.1 meV, the bound establishes a minimum decoherence time τ ~ ℏ/Δ ≈ 1.3 picoseconds, providing fundamental limitations on quantum information processing. The significance of the Nemirovsky bound extends beyond its computational utility. It serves as a unifying principle connecting quantum magnetism, topological matter, and quantum computing under a single mathematical framework. The formula establishes a bridge between microscopic quantum mechanics and macroscopic thermodynamics, explaining how discrete lattice degrees of freedom generate observable bulk properties. Moreover, it provides actionable design principles for materials engineering: maximizing m₀, minimizing coordination number z, or reducing coupling strength g all enhance the mass gap and improve stability of quantum states—crucial for developing fault-tolerant quantum technologies. This work positions the Nemirovsky bound within the broader context of constructive quantum field theory, comparing it with alternative approaches such as Perron-Frobenius theory, renormalization group methods, and mean-field approximations. While these frameworks provide existence theorems or asymptotic results, the Nemirovsky bound offers explicit quantitative predictions directly calculable from physical parameters. The structural analysis reveals hierarchical organization of physical consequences: fundamental quantum constraints (spectral gap, correlation length) determine statistical mechanical properties (partition function, free energy), which in turn manifest as measurable macroscopic observables (heat capacity, magnetic susceptibility, decoherence rates). Appendix X provides a systematic structural analysis that elucidates the Nemirovsky bound's role as a fundamental organizing principle in quantum matter. It examines the three-level hierarchical structure (quantum constraints → statistical mechanics → macroscopic observables), analyzes parameter space regimes from strong gapped to critical phases, and demonstrates cross-domain unification connecting quantum magnetism, topological materials, and quantum information theory. The appendix includes dimensional analysis confirming the formula's robustness across different lattice geometries, comprehensive comparison with alternative theoretical frameworks (Perron-Frobenius, renormalization group, mean-field theory), discussion of current limitations and possible extensions to inhomogeneous systems and many-body interactions, and exposition of the bound's conceptual significance as a bridge between scales. This structural perspective reveals the Nemirovsky bound not merely as a calculational tool, but as a conceptual framework unifying disparate phenomena through the competition between localization (m₀) and collective delocalization (2zgVmax). Future research directions include experimental verification in specific materials, extensions to inhomogeneous systems with spatially varying parameters, incorporation of many-body interactions beyond nearest-neighbor coupling, and applications to non-equilibrium quantum systems. The Nemirovsky bound represents both a practical calculation tool and a conceptual framework for understanding the rich organizational principles of gapped quantum matter. Keywords: mass gap, spectral gap, lattice quantum field theory, Nemirovsky bound, quantum phase transitions, low-temperature thermodynamics, heat capacity, partition function, quantum magnetism, topological insulators, quantum computing, decoherence, coordination number, constructive quantum field theory, spectral vacuum mechanism, correlation length, critical phenomena, quantum many-body systems, quantum-to-classical correspondence PACS: 03.65.-w (Quantum mechanics), 05.30.-d (Quantum statistical mechanics), 75.10.-b (General theory and models of magnetic ordering), 03.67.-a (Quantum information), 64.70.Tg (Quantum phase transitions) MSC2020: 81T05 (Axiomatic quantum field theory), 82B20 (Lattice systems), 81Q10 (Selfadjoint operator theory in quantum theory), 82B26 (Phase transitions)