Description: This paper introduces a thermodynamic time parameter τ = ∫C dt, where C[ρ,𝒜] quantifies the information accessibility of quantum state ρ within observable set 𝒜. We prove that entropy decrease with respect to τ is equivalent to information recovery from inaccessible degrees of freedom—a process realizable in quantum error correction (QEC) cycles. The framework predicts a measurable signature: QEC should exhibit 10-15% fidelity enhancement relative to standard quantum dynamics, arising from negative coarse-graining rates (dC/dt < 0) during syndrome measurement. The time-dependent field C(t) can be reconstructed from fidelity data via C(t) = -(1/Γ) d ln F(t)/dt, providing a falsifiable experimental observable. We present a detailed experimental protocol for trapped-ion systems, achievable with current technology. Statistical discrimination criteria distinguish this effect from conventional mechanisms (non-Markovian baths, leakage errors, SPAM errors, dynamical decoupling). The combined statistical power enables rigorous falsification. This work establishes quantum error correction as a testbed for emergent time dynamics and provides concrete predictions testable with current trapped-ion quantum computing platforms. Key contributions: Theoretical framework linking coarse-graining to emergent time Quantitative prediction: 10-15% fidelity enhancement in QEC Experimental protocol for trapped-ion systems Falsification criteria distinguishing from alternative mechanisms Document type: Preprint / Working Paper Date: December 2025
Description: This paper introduces a thermodynamic time parameter τ = ∫C dt, where C[ρ,𝒜] quantifies the information accessibility of quantum state ρ within observable set 𝒜. We prove that entropy decrease with respect to τ is equivalent to information recovery from inaccessible degrees of freedom—a process realizable in quantum error correction (QEC) cycles. The framework predicts a measurable signature: QEC should exhibit 10-15% fidelity enhancement relative to standard quantum dynamics, arising from negative coarse-graining rates (dC/dt < 0) during syndrome measurement. The time-dependent field C(t) can be reconstructed from fidelity data via C(t) = -(1/Γ) d ln F(t)/dt, providing a falsifiable experimental observable. We present a detailed experimental protocol for trapped-ion systems, achievable with current technology. Statistical discrimination criteria distinguish this effect from conventional mechanisms (non-Markovian baths, leakage errors, SPAM errors, dynamical decoupling). The combined statistical power enables rigorous falsification. This work establishes quantum error correction as a testbed for emergent time dynamics and provides concrete predictions testable with current trapped-ion quantum computing platforms. Key contributions: Theoretical framework linking coarse-graining to emergent time Quantitative prediction: 10-15% fidelity enhancement in QEC Experimental protocol for trapped-ion systems Falsification criteria distinguishing from alternative mechanisms Document type: Preprint / Working Paper Date: December 2025
Quantum thermodynamics and quantum information theory are often developed as neighboring subjects: the former studies energy, heat, work, irreversibility, and fluctuations in quantum systems, while the latter studies the representation, transmission, manipulation, and protection of information in quantum states. For fault-tolerant quantum technologies, however, the separation is artificial. A quantum memory or processor is an open, controlled, and dissipative information-processing system whose logical degrees of freedom are maintained against noise by repeated syndrome extraction, feedback, dissipation, and reset. This article develops a unifying framework in which quantum error correction (QEC) is interpreted as the stabilization of an emergent informational order in a driven nonequilibrium quantum system. The framework is organized around five common mathematical structures: density operators and quantum channels; relative entropy and nonequilibrium free energy; Gorini–Kossakowski–Lindblad–Sudarshan (GKLS) dynamics and entropy production; code subspaces, syndromes, and recovery channels; and Liouvillian spectral structure, metastability, and criticality. We show how active QEC can be viewed as an entropy-pumping cycle that transfers noise-generated uncertainty from protected degrees of freedom into syndrome and controller degrees of freedom, whose reuse requires thermodynamic reset. Continuous and autonomous QEC are formulated as competition between natural noise and engineered dissipative generators, yielding stationary or periodic nonequilibrium states with nonvanishing microscopic currents even when logical observables are approximately stationary. Complexity is introduced from the outset through multiscale organization, predictive coarse-graining, information dynamics, and spectral separation; these concepts distinguish structured persistence from entropy reduction alone. At the level of a conceptual synthesis, this perspective relates model-specific fault-tolerance thresholds to critical phenomena, logical subspaces with slow emergent manifolds, syndrome decoding with stochastic inference, and engineered dissipation with self-organization. We finally propose a thermodynamic-complexity description of QEC in terms of logical error rate, entropy-production rate, Liouvillian gap, information flow, and control power. The resulting framework provides a common language for quantum thermodynamics, nonequilibrium statistical mechanics, complexity science, and quantum information and identifies concrete questions for thermodynamically efficient fault-tolerant quantum architectures.
Entropy-Induced Collapse (EIC) is a theoretical framework that approaches the quantum measurement problem from the perspective of information recoverability. In the first paper of this series, a structural entropy threshold was introduced to separate regimes in which quantum coherence remains recoverable from those in which the information required to reconstruct coherence becomes effectively inaccessible. The second paper examined the dynamical processes leading toward this threshold, describing how system–environment interactions progressively disperse phase information across environmental degrees of freedom. This third paper investigates how the recoverability structure proposed by the EIC framework manifests in quantum information systems operating under quantum error correction (QEC). In such systems, environmental noise gradually reduces the recoverability of encoded quantum information, while QEC recovery operations attempt to restore coherence. Within this regime, transient events may occur in which quantum coherence appears to collapse locally but remains, in principle, recoverable through appropriate recovery operations. These transient phenomena are referred to as false-collapse events. The paper develops a statistical framework describing how environmental entropy growth, noise processes, and periodic QEC recovery cycles interact to produce such events. By introducing a recoverability function and analyzing entropy-driven information dispersal in open quantum systems, the work derives statistical conditions under which apparent collapse-like behavior may emerge without violating the underlying unitary evolution of the global quantum state. The analysis establishes a conceptual bridge between the foundations of the quantum measurement problem and experimentally accessible quantum information platforms. In particular, the statistical signatures of false-collapse events may be observable in modern quantum processors implementing QEC, such as superconducting qubits, trapped-ion systems, and neutral-atom processors. This paper is Part III of the four-paper Entropy-Induced Collapse series: 1. Structural entropy threshold for collapse 2. Pre-threshold information recoverability dynamics 3. False-collapse statistics in quantum error correction regimes (this paper) 4. Experimental architectures and engineering tests of entropy-based collapse diagnostics
Quantum channels generally reduce the distinguishability of quantum states, thereby constraining information transmission and processing in open quantum systems. While it is known that distinguishability can be partially recovered through suitable post-processing protocols, a systematic characterization of the maximal achievable gain has remained elusive. Here, we establish a general framework to determine and optimize the recovery of distinguishability induced by a quantum channel. We introduce an algorithm that identifies the optimal implementation of a multi-copy coarse-graining protocol applicable to arbitrary channels. Within this framework, we derive a general upper bound on the attainable distinguishability gain and quantify the performance of the protocol through its tightness relative to this bound. Our results show that collective coarse-graining can lead to effective dynamics exhibiting the operational signatures of essential non-Markovianity even when the underlying microscopic dynamics remain weakly non-Markovian. A detailed analysis reveals a nontrivial trade-off between mathematical optimality (bound saturation) and operational optimality, together with a strong dependence on both the input ensemble and the number of copies. Taken together, these findings provide a unified and quantitative framework to assess, optimize, and interpret distinguishability recovery in open quantum systems while showing how collective processing can qualitatively modify the operational memory properties of effective dynamical descriptions.
This repository contains a short technical note that isolates a single, experimentally testable signature related to quantum error correction (QEC). The work focuses on the scaling behavior of false-collapse probability under QEC, defined as the probability that a collapse-like event is inferred while logical information remains preserved. It shows that non-Markovian environmental correlations, characterized by a Hurst index H, lead to a distinct scaling behavior and a dynamic threshold shift that cannot be reproduced by Markovian decoherence models or by spontaneous localization frameworks such as GRW or CSL. The scope of this work is intentionally narrow. It makes no ontological claims about wavefunction collapse, introduces no new hardware assumptions, and provides a clearly stated falsification criterion based on scaling exponents and threshold behavior. All proposed tests are compatible with existing QEC platforms, including superconducting qubits and trapped-ion systems. The purpose of this note is not to present a comprehensive theory, but to formulate one concrete, discriminable question that can be addressed using current experimental capabilities. #QuantumErrorCorrection#NonMarkovianNoise#QuantumComputing#QuantumInformation#NoiseCorrelations#FalseCollapse#ScalingLaws#QuantumMeasurement
The definition of entropy in both classical and quantum contexts relies on a coarse-graining of the underlying microscopic description. While this dependence is widely acknowledged, the physical constraints that determine which coarse-grainings are admissible are rarely made explicit. This issue becomes particularly acute when the universe is treated as a closed system, where no external observer or privileged level of description can be assumed. Any characterization of entropy — including claims about the low-entropy initial conditions of the universe — must then be grounded in descriptions that can be physically instantiated from within the system itself. In this work, we introduce a rigorous operational framework that establishes explicit physical selection principles over the space of admissible descriptions. We organize these criteria into necessary conditions (local accessibility and physical implementation via internal interactions) and practical sufficiency conditions (finite resource requirements anchored in Landauer’s principle, dynamical stability, and effective consistency). To demonstrate the validity of our framework, we introduce a concrete one-dimensional spin-chain toy model, illustrating how mathematically valid global partitions fail to be physically realizable due to dynamic propagation limits and informational constraints. We analyze the far-reaching implications of this restriction across three domains. In classical statistical mechanics, it limits the arbitrariness of macrostate definitions. In quantum theory, it identifies environment-induced decoherence (einselection) not merely as a formal tool, but as the objective dynamical mechanism that forces the emergence of admissible internal partitions. In cosmology, it resolves foundational circularities in the quasi-classical histories framework and reframes the thermodynamic arrow of time as a "doubly relational" property—dependent both on cosmic boundary conditions and on the material limits of internal subsystems. Our framework clarifies the operational status of entropy as an emergent property of physically instantiated descriptions within a universe that observes itself.
We build a framework for the thermodynamics of macroscopic quantum systems. In contrast with approaches requiring access to the full density matrix, our framework relies on a coarse-grained description, based on measurement statistics of a few observables. When these observables commute, the outcomes define classical macrostates whose entropy is quantified by observational entropy, accounting for uncertainty about both the macrostate and the microstate within it. We extend this notion to non-commuting observables forming a subalgebra of the operator space, and use Jaynes' principle to define an algebra-dependent entropy interpolating between von Neumann and observational entropies. Given initial and final measurement sets, connected by internal and/or environment-induced dynamics, we derive a second law for the coarse-grained dynamics. Unlike formulations based on von Neumann entropy, our inequality captures irreversibility from both non-unitary environment-induced dynamics and internal equilibration. It takes the usual form of a positive entropy production when the system is initially at internal equilibrium, while correction terms capture nonequilibrium resources ignored by the coarse-graining. We also derive fluctuation theorems for coarse-grained thermodynamic quantities. Along a quasi-static path of measurement schemes, we identify quantum macroscopic notions of work and heat fulfilling the first and second laws, including an additional work contribution from manipulating the algebra to which the system is confined, through external constraints or quantum measurement backaction. Finally, we apply our framework to examples illustrating the impact of varying the coarse-graining scheme. Our approach unifies macroscopic and stochastic thermodynamics in a genuinely quantum framework, laying the basis for a versatile, experimentally friendly toolbox to analyze complex quantum dynamics.