| viXra.org > Thermodynamics and Energy > 2512 |
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| viXra.org > Thermodynamics and Energy > 2512 |
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[2] viXra:2512.0051 [pdf] submitted on 2025-12-11 00:45:43
Authors: Ilya Shesterikov
Comments: 10 Pages. (Note by viXra Admin: Please cite and list scientific references and submit article written with AI assistance to ai.viXra.org)
The canonical (Gibbs) distribution is widely used in statistical physics to describe the probabilities of microscopic states characterized by an energy value. In symbolic dynamics and the study of symbolic sequences generated by nonlinear dynamical systems, an analogous construction is frequently applied: the probability of observing a particular symbol sequence is assumed to depend exponentially on an associated "energy", often defined through a cylinder length or a Jacobian-based quantity. While this analogy is technically appealing and mathematically consistent, it has led to a persistent conceptual misunderstanding. The confusion arises when the discrete cylinder lengths are mistakenly interpreted as samples from a continuous distribution, leading to the use of probability density functions where only discrete probabilities are appropriate. In this paper, we analyze the origin of this misunderstanding, clarify the correct interpretation of the canonical distribution in symbolic dynamics, and provide practical guidance for avoiding associated pitfalls. We further illustrate the issue with examples, graphical explanations, and a discussion of implications for numerical studies of chaotic systems.
Category: Thermodynamics and Energy
[1] viXra:2512.0021 [pdf] submitted on 2025-12-05 21:46:49
Authors: Mihro J. Wen-Gray
Comments: 41 Pages. (Note by viXra Admin: Please submit article written with AI assistance to ai.viXra.org)
We present a reformulation of fundamental physics in which temporal evolution emerges fromgeometric correlations across an information-theoretically motivated foliation of spacetime. The framework is defined on a four-dimensional Lorentzian manifold (M,gAB ) equipped with a scalar entropy field swhose level sets define "entropic layers." Quantum states are represented as sections of a Hilbert bundle over this foliation, with dynamics governed by a single timeless constraint ˆequationCΨ = 0 that encodes geometric flow via an operator-valued connection Dw.We prove a correspondence theorem demonstrating that in the semiclassical weak-layer regime (ε:= |gAB ∇As∇B s|≪1), the framework reproduces Einstein’s field equations and the Schr¨odingerequation relative to any observer-chosen relational clock c= C[s]. The kinetic coefficient Z(s) of the entropy field is uniquely determined by the Fisher information metric of local probability distribu-tions, connecting continuum dynamics to information geometry and distinguishing this framework from generic scalar-tensor theories.Phenomenological predictions include Yukawa-type corrections to Newtonian gravity with cou-pling strength and range constrained by fifth-force experiments (|α|< 10−2 for λs ∼1 mm), geo-metric Berry phases in atom interferometry, curvature-induced decoherence from bundle geometry, and effective dark-energy behavior in cosmology. We compare the framework to Wheeler-DeWitt theory, Page-Wootters relational mechanics, shape dynamics, and entropic gravity approaches, clarifying both conceptual similarities and essential mathematical differences. The framework provides aunified geometric substrate for gravity, quantum mechanics, and thermodynamics without invokingfundamental time as a primitive element.
Category: Thermodynamics and Energy
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