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Thermodynamics of Information in Dissipative Projectile Motion: A Dual Lagrangian Approach Unifying Energy and Entropy Balances

Year: 2026
Type: preprint
Abstract: This paper reinterprets the mechanics of projectile motion with quadratic aerodynamic drag through the lens of non-equilibrium thermodynamics and information theory. Rather than treating aerodynamic drag merely as mechanical energy loss, we develop dual augmented Lagrangians (L_S^* and L_I^*) that unify macroscopic energy and entropy balances within a single variational framework. By reformulating the system in both thermodynamic and purely informational terms, a conceptual duality is established. The resulting variational saddle-point represents a dynamic compromise: it balances the natural drive to rapidly erase the system's initial kinematic state against the intrinsic mechanical and thermodynamic inertia that resists instantaneous dissipation. Applying this framework, analytical results reveal that the classical bounded parabolic flight is fundamentally an incomplete thermodynamic transient. Entropy production is non-homogeneous throughout the trajectory, as we find that the optimal launch angle for maximum horizontal range does not correspond to a global thermodynamic extremum. Instead, this geometric optimum is a parametric artefact forced by the ground impact, which arbitrarily truncates the system's natural phase-space evolution toward its steady-state attractor, the terminal velocity. Ultimately, this framework proves that the continuous phase-space contraction and erasure of macroscopic kinematic information imposes an unavoidable cubic thermodynamic tax on the environment. By explicitly correlating mechanical dissipation with informational loss, we establish a firm macroscopic connection between classical mechanics, non-equilibrium thermodynamics, and the physics of information.
DOI: 10.20944/preprints202610.0450.v1
Language: English
Open Access status: green
OpenAlex ID: W7221172253
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