We derive the statistical mechanics of knowledge systems, demonstrating that information undergoes phase transitions governed by the same thermodynamics as physical matter. Knowledge crystallization, decoherence, and interference are natural consequences of conservation-bounded epistemic dynamics. Paper T4.
Beginning with Mandelbrot’s insight that Fisher information may admit a thermodynamic interpretation, a growing body of work has connected this information-theoretic measure to fluctuation–dissipation relations, thermodynamic geometry, and phase transitions. Yet, these connections have largely remained at the level of formal analogies. In this work, we provide what is, to our knowledge, the first explicit realization of the epistemic-to-physical transition of Fisher information within a finite interacting quantum system. Specifically, we analyze a model of N fermions occupying two degenerate levels and coupled by a spin-flip interaction of strength V, treated in the grand canonical ensemble at inverse temperature β. We compute the Fisher information FN(V) associated with the sensitivity of the thermal state to changes in V, and show that it becomes an observer-independent, experimentally meaningful quantity: it encodes fluctuations, tracks entropy variations, and reveals structural transitions induced by interactions. Our findings thus demonstrate that Fisher information, originally conceived as an inferential and epistemic measure, can operate as a bona fide thermodynamic observable in quantum many-body physics, bridging the gap between information-theoretic foundations and measurable physical law.
This paper constructs a four-tier axiomatic system of the stability ladder toreveal the underlying logic of phase transitions in statistical mechanics. Startingfrom information conservation (L0) and short-range interactions (L1), we rigorously prove, using DLR measure theory and large deviation principles in the thermodynamic limit, that the coexistence of macroscopically distinguishable states insystems of spatial dimension not less than two necessarily requires a strictly positiveenergy barrier in the free energy landscape (L2). In one-dimensional systems, information protection is instead realized via topological boundary conditions. Takingthe two-dimensional Ising model as a paradigm, we reconstruct the ontological basisof the existence of a phase transition in Onsager’s exact solution from the axioms,and extend the framework to general lattice systems and quantum many-bodymodels. The derivation does not rely on mean-field approximations or specific calculations of the renormalization group, thereby providing a necessary explanationfor the universality of phase transitions based on the logic of information conservation. In critical dynamics and quantum phase transitions, the barrier conceptis generalized to a dynamical barrier or quantum gap, demonstrating the broaderapplicability of the stability ladder.
Fundamentals of statistical physics: the lectures - a survey one particle and many Gaussian distributions quantum mechanics and lattices. Random dynamics: diffusion and hopping from hops to statistical mechanics correlations and response. More statistical mechanics: statistical thermodynamics Fermi, Bose, and other. Phase transitions: overview of phase transitions mean field theory of critical behaviour continuous phase transitions renormalization in one dimension real space renormalization techniques duality planar model and Coulomb systems XY model, renormalization and duality.
The quantum–classical transition is one of the most frequently invoked concepts in modern physics. Yet the notion of classicality itself is far from unique. Depending on the physical context, classical behavior may be associated with decoherence, the semiclassical limit, thermodynamic averaging, suppression of correlations, emergence of collective order, or geometric simplification of statistical state space. These viewpoints are often presented as if they described a single phenomenon, although they emphasize different physical mechanisms and different operational criteria. In this article we examine the principal notions of classicality that appear across quantum theory, statistical physics, condensed matter physics, and information geometry. We compare the corresponding mechanisms of classical emergence and analyze the physical quantities commonly used to characterize them, including coherence, entanglement, fluctuations, correlation length, Fisher information, statistical complexity, and information-geometric curvature. We argue that many apparently distinct routes toward classical behavior share a common structural feature: a reduction of effective fluctuation freedom. From this perspective, classicality may be interpreted as an emergent regime in which the accessible fluctuation manifold becomes progressively constrained, stabilized, or geometrically simplified. This viewpoint naturally unifies decoherence, semiclassical localization, thermodynamic averaging, decorrelation, and collective organization within a common conceptual framework. Rather than representing a unique physical process, the quantum–classical transition appears as a family of related mechanisms through which complex quantum fluctuation structure gives rise to effective macroscopic classical behavior.
This innovative and modular textbook combines classical topics in thermodynamics, statistical mechanics and many-body theory with the latest developments in condensed matter physics research. Written by internationally renowned experts and logically structured to cater for undergraduate and postgraduate students and researchers, it covers the underlying theoretical principles and includes numerous problems and worked examples to put this knowledge into practice. Three main streams provide a framework for the book; beginning with thermodynamics and classical statistical mechanics, including mean field approximation, fluctuations and the renormalization group approach to critical phenomena. The authors then examine quantum statistical mechanics, covering key topics such as normal Fermi and Luttinger liquids, superfluidity and superconductivity. Finally, they explore classical and quantum kinetics, Anderson localization and quantum interference, and disordered Fermi liquids. Unique in providing a bridge between thermodynamics and advanced topics in condensed matter, this textbook is an invaluable resource to all students of physics.