The Anatomical Foundations of Statistical Mechanics: Epistemology, Ontology, and Quantum Transitions (Vol-I)
Syed Muntasir Mamun
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
•Jan 1, 2026•0 citations