A fundamental gap in quantum thermodynamics is resolved through the derivation of a single operational constraint that closes information gain, memory cost, and measurement back-action into a unified informational budget. It is demonstrated that bandwidth-limited acquisition and measurement-driven control emerge as fundamental consequences of this budget. A universal Critical Bandwidth is identified, marking the threshold where classical dissipation necessitates a transition to quantum-entangled states. This framework is validated by an empirical audit of the human cortex, identifying a 35:1 communication-to-computation energy ratio as the definitive thermodynamic signature of the Entanglement Heat Premium. The discovery of a scale-invariant efficiency constant, establishes the human brain as a near-optimal quantum-limited engine. These results provide a unified scaling law for the energetic limits of intelligence, bridging the gap between superconducting qubits and biological consciousness.
A fundamental gap in quantum thermodynamics is resolved through the derivation of a single operational constraint that closes information gain, memory cost, and measurement back-action into a unified informational budget. It is demonstrated that bandwidth-limited acquisition and measurement-driven control emerge as fundamental consequences of this budget. A universal Critical Bandwidth is identified, marking the threshold where classical dissipation necessitates a transition to quantum-entangled states. This framework is validated by an empirical audit of the human cortex, identifying a 35:1 communication-to-computation energy ratio as the definitive thermodynamic signature of the Entanglement Heat Premium. The discovery of a scale-invariant efficiency constant, establishes the human brain as a near-optimal quantum-limited engine. These results provide a unified scaling law for the energetic limits of intelligence, bridging the gap between superconducting qubits and biological consciousness.
This is a preliminary study and not the final version. An updated revision will be available shortly. We thank you for your feedback. Quantum V-Index: A Universal Efficiency Metric for Information Processing While classical thermodynamics defines the theoretical minimum cost of information erasure via Landauer’s principle, real-world physical systems ranging from nanomagnetic bits to quantum circuits operate with a consistent overhead to maintain informational integrity. This paper introduces the Quantum V-Index (Vq), a dimensionless metric that unifies von Neumann entropy, energy dissipation, and system stability into a single, platform-independent framework. By normalizing physical variables into bit-equivalents, the V-index reveals a fundamental symmetry in informational processes. At the theoretical limit of optimality, the index converges to a fixed reference point, while high-precision experimental data across diverse platforms suggest the existence of a universal stability constant.This framework bridges the gap between quantum coherence and classical dissipation, providing an objective benchmark for qubit operation efficiency and informational integrity. The Quantum V-Index represents a candidate for a universal law of informational thermodynamics, defining the precise energy entropy cost of stability in any processing system. Note: In quantum thermodynamic treatments the definition of ΔS_Q can follow either a system‑based or an environment‑based entropy convention. The present preprint uses one consistent convention, but readers should be aware that different frameworks assign ΔS_Q differently. A New Horizon in Quantum Gravity (V-index) The underlying mathematical formulas and the formal definition of the V-index : https://doi.org/10.5281/zenodo.18147084
Quantum reservoir computing provides a framework for processing complex temporal data, yet its fundamental computational and energetic limits remain unresolved. Here, we establish a non-equilibrium thermodynamic framework that links the macroscopic predictive performance of driven open quantum systems to their microscopic energetic costs. By mapping Holevo capacities onto the Bogoliubov-Kubo-Mori geometric manifold, we analytically prove that the computational peak within the quantum critical region originates from a spectral resonance: the closing of the intrinsic energy gap forces the reservoir's internal transition frequencies to align with the chaotic drive. To evaluate the associated thermodynamic costs, we introduce quantum informational dissipation to quantify the non-predictive historical data retained by the reservoir. This allows us to derive a generalized Landauer bound for continuous temporal processing, which reveals a fundamental thermodynamic trade-off: the critical resonance that maximizes predictive capacity simultaneously maximizes informational dissipation and the irreversible work required for environmental erasure. Furthermore, coherence decomposition demonstrates that quantum coherences amplify predictive capacity without demanding additional mechanical work. These findings establish the fundamental energetic limits of quantum learning devices, providing theoretical principles for designing energy-efficient quantum neuromorphic hardware.
The dominant paradigm for universal quantum computation, predicated on active error correction, is fundamentally constrained by a thermodynamic wall, a phase transition where the entropy produced by control operations catastrophically overwhelms the system. This study quantifies this constraint, identifying a colossal “Protection Deficit” of approximately 1012 between the metabolic efficiency of biological systems and the energy cost of state-of-the-art engineered quantum processors. To resolve this thermodynamic crisis, we propose a shift from “forced” discrete control to “geodesic” evolution on a quantum information manifold. Through a stochastic master equation simulation, we compare a high-forcing “Shor” protocol against a low-forcing “Feynman” protocol. The simulation results are definitive: the Shor protocol breaches the thermodynamic wall in microseconds, dissipating 52.5 J, while the Feynman protocol, leveraging passive protection from high topological complexity (Q=5) and chirality (λ=0.9), maintains a fidelity of >0.99 for over a second with a minimal energy cost of 4.0 J. This work refutes the “Myth of Specialization” by invoking the AQC equivalence theorem, which proves that Hamiltonian-based systems (“Feynman Matter”) are computationally universal. We argue that Feynman Matter is not a niche simulator but the only thermodynamically viable substrate for a universal quantum computer, acting as a “Layer 0” error suppression layer that makes a subsequent, minimal active code tractable. This hybrid model resolves the Feynman-Shor bifurcation, with biological intelligence, validated by recent lithium isotope experiments, serving as the ultimate existence proof of a universal geodesic computer.
This paper explores the emerging intersection of quantum thermodynamics and quantum information processing. The core argument presented is that quantum information processing fundamentally relies on the thermodynamic properties of quantum systems and can be significantly advanced by leveraging the principles of quantum thermodynamics. This work establishes a framework for analyzing and designing quantum information protocols through the lens of thermodynamic constraints and efficiencies. We introduce a novel perspective where quantum information tasks are viewed as thermodynamic processes, allowing for a more rigorous understanding of their limitations and potential optimizations. The methodology presented aims to bridge the gap between information theory and thermodynamics, ultimately leading to the development of more robust and efficient quantum information systems. Key concepts explored include quantum work, heat dissipation, entropy production, and their implications for quantum data storage, quantum computation, and quantum communication. This research contributes to a fundamental shift in how we approach quantum information processing, moving beyond purely computational considerations to incorporate the underlying thermodynamic realities of quantum systems.
Standard quantum computing models often assume that error correction can scale indefinitely regardless of operating temperature. However, the thermodynamic constraints on nanoscale systems create a fundamental energy scale mismatch at room temperature that remains unsolved by algorithmic optimizations. Here, a consilience of theoretical thermodynamics, decoherence dynamics, and experimental validation is introduced to delineate the absolute physical boundaries of quantum feasibility. By integrating the Caldeira-Leggett model with relativistic causality constraints, it is demonstrated that atomic-precision quantum computing is thermodynamically impossible above 20 Kelvin. Furthermore, it is identified that while ultra-cryogenic operation (0.1K) offers theoretical scalability, it faces severe engineering bottlenecks from wiring heat loads and thermal boundary resistance (Kapitza resistance). This finding redefines the strategic landscape of quantum computing, establishing cryogenic operation not as an engineering choice but as an immutable physical mandate constrained by thermal logistics.
A central open question in quantum thermodynamics is the identification of thermodynamic entropy away from equilibrium. Although thermodynamic entropy coincides with the von Neumann entropy for a Gibbs state at equilibrium, the thermodynamic role of quantum coherence generated during nonequilibrium evolution remains unclear. Here, we show that von Neumann entropy does not, in general, represent the thermodynamic entropy governing heat exchange in coherent nonequilibrium quantum systems. By integrating the resource theory of quantum coherence with thermodynamic principles, we develop a general framework for nonequilibrium quantum thermodynamics. We identify thermodynamic entropy with the energy entropy derived from energy-measurement statistics and introduce a dynamical temperature extending the equilibrium concept to nonequilibrium states. Consequently, we obtain an exact entropy-balance relation separating the entropy flux associated with heat exchange from the coherence-loss contribution to entropy production, establishing an operational connection between quantum coherence, heat flow, and total entropy change. Unlike approaches relying on equilibrium reference states or stationary Gibbs ensembles, our framework uses instantaneous dynamical quantities and remains valid throughout transient nonequilibrium evolution. It provides consistent dynamical definitions of temperature, work, heat, and free energy. Applying the formalism to an exactly solvable open quantum system, we show that the first and second laws hold throughout transient evolution and that equilibrium thermodynamics emerges dynamically in the weak-coupling long-time limit. Our results establish a unified framework for coherent nonequilibrium quantum thermodynamics and suggest opportunities for controlling heat dissipation through coherence engineering in quantum thermal technologies.