Relativistic Kinematics from Projected Thermodynamic State-Space Dynamics: Understanding the Thermodynamics of Jitter

Relativistic Kinematics from Projected Thermodynamic State-Space Dynamics: Understanding the Thermodynamics of Jitter | Authorea try { document.documentElement.classList.add('js'); } catch (e) { } var _gaq = _gaq || []; _gaq.push(['_setAccount', 'G-8VDV14Y67G']); _gaq.push(['_trackPageview']); (function() { var ga = document.createElement('script'); ga.type = 'text/javascript'; ga.async = true; ga.src = ('https:' == document.location.protocol ? 'https://ssl' : 'http://www') + '.google-analytics.com/ga.js'; var s = document.getElementsByTagName('script')[0]; s.parentNode.insertBefore(ga, s); })(); Skip to main content Preprints Collections Wiley Open Research IET Open Research Ecological Society of Japan All Collections About About Authorea FAQs Contact Us Quick Search anywhere Search for preprint articles, keywords, etc. Search Search ADVANCED SEARCH SCROLL This is a preprint and has not been peer reviewed. Data may be preliminary. 5 February 2026 V1 Latest version Share on Relativistic Kinematics from Projected Thermodynamic State-Space Dynamics: Understanding the Thermodynamics of Jitter Authors : Early stage exploratory work only -mn [email protected] and Madison J Newell Authors Info & Affiliations https://doi.org/10.22541/au.177031164.42013926/v1 157 views 57 downloads Contents Abstract Supplementary Material Information & Authors Metrics & Citations View Options References Figures Tables Media Share Abstract We present a constructive link between relativistic kinematics and nonequilibrium thermodynamic state-space dynamics by projecting GENERIC evolution onto a single scalar state variable identified with rapidity. Once this variable parametrizes the unit timelike four-velocity, Minkowski spacetime kinematics-including inertial motion, uniformly accelerated (Rindler) worldlines, and Lorentz-invariant velocity composition-emerge as a geometric embedding rather than a fundamental assumption [1-5]. Constant rates of change of the projected rapidity generate hyperbolic worldlines, while inertial motion arises as the vanishing-acceleration limit, establishing a direct correspondence between abstract state-space dynamics and relativistic motion [3, 4]. This framework provides a natural dynamical interpretation of relativistic radiation processes. Writing the Lorentz factor as γ = cosh θ, we show that the characteristic relativistic beaming angle scales as ∆θcone ∼ sech θ, allowing radiation formation conditions to be expressed directly in terms of rapidity variation [6, 7]. In the appendix, the standard jitter radiation criterion is reformulated as a condition on the projected GENERIC flow: jitter emission occurs when the rapidity change over a formation time satisfies ∆θ form ≳ 1/γ [ \cite{Medvedev_2000} ]. This clarifies that the distinction between jitter and non-jitter radiation is not purely kinematic, but reflects whether radiation probes non-Hamiltonian, entropy-producing components of the underlying state-space dynamics [2, 9]. The final result is a unified picture in which relativistic motion and radiation properties emerge from projected thermodynamic dynamics: smooth, Hamiltonian-dominated rapidity evolution yields conventional synchrotron-or curvature-like emission, while rapid, non-Hamiltonian fluctuations naturally give rise to jitter radiation [6, 8]. Supplementary Material File (therm_rel_grounded.pdf) Download 293.49 KB Information & Authors Information Version history V1 Version 1 05 February 2026 Copyright This work is licensed under a Non Exclusive No Reuse License. Keywords astrophysics jitter radiation plasma relativity thermodynamics Authors Affiliations Early stage exploratory work only -mn [email protected] View all articles by this author Madison J Newell Embry-Riddle Aeronautical University View all articles by this author Metrics & Citations Metrics Article Usage 157 views 57 downloads .FvxKWukQNSOunydq8rnd { width: 100px; } Citations Download citation Early stage exploratory work only -mn, Madison J Newell. Relativistic Kinematics from Projected Thermodynamic State-Space Dynamics: Understanding the Thermodynamics of Jitter. Authorea . 05 February 2026. 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