Thermodynamic Sculpting of Quantum Foundations: An Anatomical Review of Krumm et al. (2017) in the Context of Advances in Generalized Probabilistic Theories and Pathways for Hilbert Space Evolution (Vol-I)
The 2017 paper by Marius Krumm, Howard Barnum, Jonathan Barrett, and Markus P. Müller, published in New Journal of Physics, represents a landmark contribution to the foundations of quantum mechanics within the framework of generalised probabilistic theories (GPTs). By imposing two minimal thermodynamic postulates—reversible transformations between distinguishable pure states and the existence of a semi-permeable membrane distinguishing them—the authors demonstrate that key structural features of quantum theory, including self-duality of the state space, analogues of projective measurements, subspaces, and eigenvalues, emerge naturally from thermodynamic compatibility. Yet these postulates leave room for a Mamun, SM (2026)……………………………………………1 Thermodynamic Sculpting of Quantum Foundations: An Anatomical Review of Krumm et al. (2017) in the Context of Advances in Generalized Probabilistic Theories and Pathways for Hilbert Space Evolution (Vol-I) restricted class of non-quantum theories consistent with a von Neumann-style thermodynamic entropy and the second law. This review provides a thorough anatomical dissection of the paper's arguments, contrasts its findings with post-2017 developments in GPTs, quantum thermodynamics, and experimental tests of higher-order interference, and explores plausible evolutionary pathways for assessing and potentially extending the Hilbert space formalism. Also available on Academia.edu: https://www.academia.edu/attachments/132550634/download_file?s=portfolio
The 2017 paper by Marius Krumm, Howard Barnum, Jonathan Barrett, and Markus P. Müller, published in New Journal of Physics, represents a landmark contribution to the foundations of quantum mechanics within the framework of generalised probabilistic theories (GPTs). By imposing two minimal thermodynamic postulates—reversible transformations between distinguishable pure states and the existence of a semi-permeable membrane distinguishing them—the authors demonstrate that key structural features of quantum theory, including self-duality of the state space, analogues of projective measurements, subspaces, and eigenvalues, emerge naturally from thermodynamic compatibility. Yet these postulates leave room for a Mamun, SM (2026)……………………………………………1 Thermodynamic Sculpting of Quantum Foundations: An Anatomical Review of Krumm et al. (2017) in the Context of Advances in Generalized Probabilistic Theories and Pathways for Hilbert Space Evolution (Vol-I) restricted class of non-quantum theories consistent with a von Neumann-style thermodynamic entropy and the second law. This review provides a thorough anatomical dissection of the paper's arguments, contrasts its findings with post-2017 developments in GPTs, quantum thermodynamics, and experimental tests of higher-order interference, and explores plausible evolutionary pathways for assessing and potentially extending the Hilbert space formalism. Also available on Academia.edu: https://www.academia.edu/attachments/132550634/download_file?s=portfolio
We investigate the extent to which thermodynamic reasonableness, formalized as two operational postulates on entropy and reversible dynamics within the framework of Generalized Probabilistic Theories (GPTs), uniquely determines the complex Hilbert space formalism of standard quantum mechanics. Building on Krumm, Müller, and Masanes (2017), we provide an extended classification of state spaces satisfying thermodynamic consistency for systems of (N \ge 3) distinguishable states, proving that self-duality of the state cone, spectral entropy compatibility, and continuous reversible dynamics jointly eliminate real and quaternionic quantum theories as viable candidates. We show that augmenting the thermodynamic postulates with local tomographic closure and a purification principle is sufficient to recover full complex Hilbert space structure, deriving analogues of the Born rule via entropy maximization arguments. A central novel result is a no-go theorem establishing that non-complex state spaces cannot support a continuous, reversible, and entropy-preserving dynamics compatible with thermodynamic equilibration in composite systems. We further propose experimentally falsifiable signatures of post-quantum deviations using higher-order interference, generalized Landauer erasure, and multi-slit protocols. Also available on Academia.edu: https://www.academia.edu/attachments/132550729/download_file?s=portfolio
K SC This essay provides an exhaustive review and anatomical critique of the foundational structures of statistical mechanics, a discipline defined by the enduring dualism between Boltzmannian (BSM) and Gibbsian (GSM) frameworks. The analysis establishes a detailed ontological and epistemological comparison, arguing that while the Gibbsian ensemble provides mathematical universality for condensed matter physics, it fundamentally fails to explain isolated irreversibility without resorting to subjective "coarse-graining". Conversely, BSM offers a more objective, phase-space-based explanation for the arrow of time, despite its complexity with interacting particles. The essay further explores the critical touchpoints with quantum mechanics, highlighting the Eigenstate Thermalization Hypothesis (ETH) as a transformative mechanism where thermal properties are inherently embedded within individual chaotic quantum eigenstates. This resolves the limitations of classical ergodicity and enables isolated quantum systems to self-thermalize. Future research trajectories are projected across classical and quantum domains, focusing on Stochastic Thermodynamics, non-equilibrium memory effects, and Quantum Resource Theories. KSCCN Mamun, SM (2026)................................................1 The Anatomical Foundations of Statistical Mechanics: Epistemology, Ontology, and Quantum Transitions (Vol-I) Also available on Academia.edu: https://www.academia.edu/attachments/132948610/download_file?s=portfolio
Despite its unparalleled empirical success, the standard formalism of quantum mechanics, strictly bound to complex Hilbert spaces, raises profound foundational questions regarding its axiomatic origins. Among the most enduring mysteries is why quantum theory permits pairwise, second-order interference, yet strictly forbids genuine higher-order multi-path interference. While Rafael Sorkin's quantum measure theory formalized this absence of higher-order interference mathematically, a comprehensive physical justification rooted in thermodynamics has remained elusive. This report provides an exhaustive analysis bridging Sorkin's hierarchy of interference with operational thermodynamics within the framework of Generalized Probabilistic Theories (GPTs). Building upon Krumm et al.'s seminal Theorem 12—which establishes a strict equivalence between the absence of third-order interference and the coincidence of measurement and decomposition max-entropies—this paper generalizes the Mamun, SM (2026) ……………………………….1 Higher-Order Interference and Thermodynamic Entropy in Generalized Hilbert Spaces Bridging Sorkin's Framework with Operational Thermodynamics (Vol-III) equivalence to arbitrary-order Rényi entropies across non-Hilbert state spaces. Also available on Academia.edu: https://www.academia.edu/attachments/132551016/download_file?s=portfolio
K SC This paper presents a detailed anatomical review of Roger Balian's 2005 tutorial essay "Information in statistical physics" (arXiv:cond-mat/0501322). Balian systematically reconstructs the foundations of quantum statistical mechanics from the dual premises of incomplete controllability of microscopic variables and the maximisation of von Neumann entropy under linear constraints. The central conceptual innovation is the notion of relevant entropy associated with a chosen set of relevant observables; irreversibility then appears as an irreversible leakage of information from relevant into irrelevant degrees of freedom. The review dissects the argument section by section, enumerates strengths and limitations, situates the framework against at least ten competing information-theoretic and thermodynamic models (Jaynes MaxEnt, Boltzmann H-theorem, Tsallis and Rényi entropies, quantum Darwinism, eigenstate thermalisation, stochastic thermodynamics, resource theories, maximum caliber, consistent histories, and algorithmic information), and examines the ontological and epistemological verticals that underwrite the evolution of the central themes. Possible extensions toward open quantum systems, quantum information thermodynamics, and algorithmic randomness are indicated. Also available on Academia.edu: https://www.academia.edu/attachments/133857939/download_file?s=portfolio
Despite its enormous empirical success, the formalism of quantum theory still raises fundamental questions: why is nature described in terms of complex Hilbert spaces, and what modifications of it could we reasonably expect to find in some regimes of physics? Here we address these questions by studying how compatibility with thermodynamics constrains the structure of quantum theory. We employ two postulates that any probabilistic theory with reasonable thermodynamic behaviour should arguably satisfy. In the framework of generalised probabilistic theories, we show that these postulates already imply important aspects of quantum theory, like self-duality and analogues of projective measurements, subspaces and eigenvalues. However, they may still admit a class of theories beyond quantum mechanics. Using a thought experiment by von Neumann, we show that these theories admit a consistent thermodynamic notion of entropy, and prove that the second law holds for projective measurements and mixing procedures. Furthermore, we study additional entropy-like quantities based on measurement probabilities and convex decomposition probabilities, and uncover a relation between one of these quantities and Sorkin’s notion of higher-order interference.