This manuscript proposes a dual-field Lagrangian framework where particle mechanics emerges from the interaction between a real scalar field (x, t) and a dynamical entropy field (x, t). By treating entropy as a geometric degree of freedom, we derive a unified action that accounts for both conservative and dissipative dynamics, recovering Newtonian mechanics as a special decoherent limit. The framework establishes a thermodynamic metric g₈₉ = ₈₉/ (x), where friction emerges as a consequence of Ricci curvature. We provide explicit, falsifiable predictions for Bose-Einstein condensates (BECs) in temperature gradients, including a relative center-of-mass displacement of 8 3~ and a unique ^-1 frequency scaling signature. With a calculated Signal-to-Noise Ratio (SNR) of 6. 4, the framework offers a clear experimental pathway for distinguishing entropy-modulated dynamics from classical backgrounds such as gravity and thermophoresis.
Lohith Lohith (Tue,) studied this question.