The Reversibility Cost Theorem: Thermodynamic Limits on Unitary Evolution in Complex Systems

Standard quantum mechanics posits unitary, time-reversible evolution at the fundamental level, with irreversibility emerging only statistically. This paper challenges that paradigm by introducing the Reversibility Cost Theorem. We prove that for a finite interacting system of size N, the computational cost of maintaining the information necessary for microscopic reversibility scales as C(N) ~ e^(αN). We demonstrate the existence of a critical complexity threshold Nc, beyond which the thermodynamic cost of information storage exceeds the system's stability limit. Consequently, macroscopic asymmetry is not an artifact of coarse-graining but a fundamental thermodynamic necessity. We derive a quantitative prediction for the resulting Thermodynamic Drag (ε), a strictly positive deviation from the Jarzynski equality, and calculate testable values for mesoscopic biological motors.