Complexities

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.

Generalized Schelling models extend the classical relocation framework by introducing additional agent attributes, interaction rules, and mobility constraints. We study four variants within a common lattice formulation: a modified movement-only baseline, a local affiliation-interaction model, a model with local and random long-range interactions, and a monetary model in which movement and communication consume resources. The simulations use a $64\times 64$ lattice and are evaluated over 30 independently seeded runs per scenario, with means and 95% confidence intervals reported throughout. At each step, occupied agents are classified as bound, activated, or, in the monetary scenario, trapped. Their conditional affiliation distributions are evaluated using Shannon entropy and a shape-weighted diagnostic whose fitted components distinguish normal-like, heavy-tailed, and bimodal structures. The diagnostic is interpreted jointly with its fitted weights and the underlying histograms rather than as a unique scalar reconstruction of shape. Validation against the bimodality coefficient, Esteban–Ray polarization, Moran’s I, and sign assortativity separates distributional polarization from spatial segregation. The interaction-driven scenarios develop strongly polarized two-lobed bound-state distributions, while the monetary model additionally produces resource-constrained dynamical arrest. The results are robust across independent initial conditions and random streams; separate extended-horizon checks to 500 steps showed no qualitative reversal. The same regimes persist on $96\times 96$ and $128\times 128$ lattices and under one-factor variations of satisfaction, vacancy, long-range-contact, and monetary-cost parameters. The framework therefore complements Shannon entropy by exposing distributional geometry that uncertainty alone does not encode.

Decision theories based on cognitive consistency understand decision-making as the process of constructing a coherent representation of reality, capable of providing a reliable causal map that connects actions to consequences. Rejecting assumptions concerning preferences and utility functions, they single out the quest for a coherent representation of reality as the one single factor driving human behaviour. Decision theories based on constructing coherence are justified by free-energy minimisation and supported by computational network models, but they lack a proper mathematical framework. In this article I combine Evidence Theory with Quantum Logic to offer a scaffolding structure to construct coherent representations. I illustrate this framework with stylised examples drawn from medical diagnoses and the BioTech industry.