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
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
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
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
This paper synthesizes the "Anatomical Reviews" to redefine the quantum-classical transition through an intrinsic operator-algebraic framework. It moves away from standard environment-induced decoherence toward a model where classicality emerges from the sectorisation of infinite-dimensional Hilbert spaces within isolated systems. Utilizing the Avalanche Photodiode (APD) model, the study demonstrates that macroscopic definiteness arises from double-exponential divergence in state overlap, creating a rigorous structural transition. The work formalizes this transition as a geometric degeneracy in the quantum Fisher information metric, linking fractal avalanche geometry to Tomita-Takesaki modular theory and providing a falsifiable experimental foundation for the algebraic Heisenberg cut. KSCCN Mamun, SM (2026) ……………………………….1 Algebraic Sectorisation, Information Geometry, and the Quantum-Classical Transition A Synthesis of the Anatomical Reviews (Vol-VI) Also available on Academia.edu: https://www.academia.edu/attachments/133083183/download_file?s=portfolio
This ninth volume closes a critical gap in post-quantum cryptography (PQC) by deriving hybrid, thermodynamic-augmented security reductions for lattice-based architectures. The work shifts the definition of cryptographic resilience from model-relative computational assumptions (Tier-1) to a physically conserved resource strictly bounded by the irreversible laws of thermodynamics and fractal phase-space geometry (Tier-2). The proposed construction, Thermodynamic-LWE (T-LWE), mandates noise generation via physically irreducible Enclave-Oracle Physical Unclonable Functions (PUFs) and utilizes heavy-tailed Lévy/Cauchy distributions to enforce physical interaction limits. By integrating Landauer's principle for the cost of quantum Mamun, SM (2026) …………………………….1 Theoretical and Physical Boundaries of Lattice-Based Post-Quantum Cryptography: An Anatomical Critique of Thermodynamic Entropy Bounds Integrated into Security Reductions (Vol-IX) K S C state preparation and the Fannes-Audenaert inequality for von Neumann entropy continuity, the analysis proves that any quantum adversary attempting sophisticated extraction algorithms incurs a non-bypassable information-theoretic penalty. This penalty is exponentially amplified by the multifractal topology (Df) of the noise distribution. The resulting framework furnishes the global cryptographic community with deployable, entropy-augmented security proofs, anchoring quantum resilience to immutable physical laws. Also available on Academia.edu: https://www.academia.edu/attachments/132780724/download_file?s=portfolio
The act of measuring a system has profound consequences of dynamical and thermodynamic nature. In particular, the degree of irreversibility ensuing from a nonequilibrium process is strongly affected by measurements aimed at acquiring information on the state of a system of interest: the conditional and unconditional entropy production, which quantify the degree of irreversibility of the open system's dynamics, are related to each other by clearly interpreted informational quantities. Building on a recently proposed collisional model framework [G. T. Landi, M. Paternostro, and A. Belenchia, PRX Quantum 3, 010303 (2022)], we investigate the case of continuous-variable information carriers prepared in Gaussian states and undergoing Gaussian processes. We build up a toolbox that fully characterizes the thermodynamics of continuously measured nonequilibrium Gaussian systems and processes, illustrating how the instruments hereby introduced provide key insight into recent experiments on mesoscopic quantum systems [M. Rossi, L. Mancino, G. T. Landi, M. Paternostro, A. Schliesser, and A. Belenchia, Phys. Rev. Lett. 125, 080601 (2020)].
This report constructs a rigorous theoretical bridge connecting the deterministic evolution of isolated quantum systems, governed by the Hamiltonian operator, with the irreversible, macroscopic thermalization demanded by the second law of thermodynamics. It utilizes the Eigenstate Thermalization Hypothesis (ETH) to reconcile this contradiction, asserting that individual energy eigenstates are intrinsically thermal. To transcend ETH's descriptive limits, the Statistical Jacobi Approximation (SJA) is introduced to predict far-from-equilibrium dynamics and response functions following quantum quenches without requiring complete re-diagonalization. The document demonstrates that multiscale energy transfer, specifically the inverse energy cascade mediated by recursive zig-zag patterns observed in classical turbulence, persists within microscopic quantum superfluids and optical lattices. Critically, to stress-test these frameworks, the report employs fractal geometries as advanced simulational incubators. Fractals, by Mamun, SM (2026) ………………………….1 Quantum Mechanics, the Hamiltonian, and Thermodynamics: Predicting Eigenstates via Fractal Simulations (Volume II) K S C breaking translational symmetry, lead to the emergence of non-ergodic multifractal (NEM) states that actively defy ETH, and provide empirical validation through the high-resolution observation of Hofstadter's Butterfly in moiré superlattices. Also available on Academia.edu: https://www.academia.edu/attachments/132683179/download_file?s=portfolio