Memory Inverse Multiplicative by Octávio Teodoro

Classical algebra assumes exact symmetry in inversion (X * X^{-1} = 1), but physical, computational, and biological systems always incur hidden costs when reversing states. This paper introduces the Residual Constant \Lambda and the concept of Multiplicative Inverse Memory to quantify this asymmetric overhead. By leveraging the Jarzynski-Crooks fluctuation theorem, we derive a universal thermodynamic lower bound for reversal costs based on Kullback-Leibler divergence. For Gaussian distributions, this bound scales directly with the square of the system’s signal-to-noise ratio: delta{min} = 2k * T * (SNR)^2. Finally, the framework is validated via Monte Carlo simulations and mapped onto practical applications, including CMOS energy dissipation, blockchain rollbacks, and biochemical signaling cascades.