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
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
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
Landi and Paternostro (2022) deliver a comprehensive, bottom-up synthesis of irreversible entropy production (Σ) that unifies classical thermodynamics, stochastic thermodynamics, open quantum systems, quantum information theory, and resource-theoretic thermodynamics. At its core lies a single, operationally transparent formula derived from global unitary evolution of an initially uncorrelated system-environment state: [ \Sigma = I_{\rho'{SE}}(S:E) + S(\rho'E | \rho_E) \geq 0, ] where (I{\rho'{SE}}(S:E)) is the mutual information generated between system (S) and environment (E) after the interaction, and (S(\rho'_E | \rho_E)) KSCCN REVIEW MAMUN, SM (2026)…………………………………………………………..1 Critical Anatomical Review of "Irreversible Entropy Production, from Quantum to Classical" by Landi and Paternostro (2022) is the relative entropy quantifying how far the environment is driven from its initial state. The authors meticulously unpack the mechanics of this expression—its reduction to the Clausius form for thermal baths, its fluctuation-theorem interpretations under multiple backward protocols, its emergence in collisional models that recover the classical limit, and its reconciliation with thermo-majorization and second laws of resource theories. Also available on Academia.edu: https://www.academia.edu/attachments/132718642/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
This paper undertakes an anatomical review of J. Harlow's LinkedIn essay of 25 September 2026, which poses the question why one should privilege John von Neumann's Mathematische Grundlagen der Quantenmechanik (1932; English 1949/1955) over P. A. M. Dirac's The Principles of Quantum Mechanics (1930 and later editions). The source text constructs a binary lineage: a Dirac–Jordan 'continuum tradition' of amplitudes, delta functions and infinitesimal smoothness, versus a von Neumann–Wigner–Turing–Bardeen 'finite-state' operator tradition alleged to underwrite semiconductor physics, BCS theory and even ASML lithography. The review reconstructs the essay's claims, rhetoric and tacit epistemology; compares them with the actual mathematical relationship between Dirac calculus and Hilbert-space operator theory; and contrasts both with the leading contemporary accounts of measurement, representation and emergence—Copenhagen hybrids, decoherence and einselection, Everett, de Broglie–Bohm, objective-collapse models, QBism and relational views, consistent histories, algebraic quantum field theory, information-theoretic reconstructions, and discrete spacetime or quantum-automaton programmes. The principal finding is that the essay's dichotomy is historically suggestive but technically overstated. Also available on Academia.edu: https://www.academia.edu/attachments/134519177/download_file?s=portfolio
We review with a tutorial scope the information theory foundations of quantum statistical physics. Only a small proportion of the variables that characterize a system at the microscopic scale can be controlled, for both practical and theoretical reasons, and a probabilistic description involving the observers is required. The criterion of maximum von Neumann entropy is then used for making reasonable inferences. It means that no spurious information is introduced besides the known data. Its outcomes can be given a direct justification based on the principle of indifference of Laplace. We introduce the concept of relevant entropy associated with some set of relevant variables; it characterizes the information that is missing at the microscopic level when only these variables are known. For equilibrium problems, the relevant variables are the conserved ones, and the Second Law is recovered as a second step of the inference process. For non-equilibrium problems, the increase of the relevant entropy expresses an irretrievable loss of information from the relevant variables towards the irrelevant ones. Two examples illustrate the flexibility of the choice of relevant variables and the multiplicity of the associated entropies: the thermodynamic entropy (satisfying the Clausius–Duhem inequality) and the Boltzmann entropy (satisfying the H-theorem). The identification of entropy with missing information is also supported by the paradox of Maxwell’s demon. Spin-echo experiments show that irreversibility itself is not an absolute concept: use of hidden information may overcome the arrow of time.
Building directly upon Volume I of this series, the present volume undertakes a rigorous mathematical dissection of the emergent von Neumann algebraic structure arising in the infinite-tensor-product (ITP) limit of the avalanche-photodiode model introduced by Van Den Bossche and Grangier (2025). We focus on the precise classification of the centre Z(M) of the type-III von Neumann algebra M generated by the limiting sector parameters. The centre is shown to be a non-trivial abelian von Neumann algebra, isomorphic to L∞ (Ω, µ) where Ω is the space of superselection sectors. We then explore natural embeddings of this centre into the framework of quantum information geometry, interpreting the sector parameters as coordinates on a statistical manifold equipped with the quantum Fisher information metric. Finally, we recast the entire construction within non-commutative probability theory, exhibiting a faithful conditional expectation onto the centre and discussing its implications for the modular automorphism group and the algebraic Heisenberg cut. All arguments remain faithful to the concrete APD dynamics while extending the original analysis into the rich territory of operator algebras, differential geometry on state spaces, and quantum probability. K 1 S Also available on Academia.edu: https://www.academia.edu/attachments/133072735/download_file?s=portfolio