Revealing Dissipation as Causal Memory Storage in Linear and Nonlinear Systems: QSER Application

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Isah M. A., Muhammad A.

The Tenth International Conference on Computational Mathematics and Engineering Sciences (CMES-2026) , İstanbul, Türkiye, 24 - 26 Nisan 2026, ss.97, (Özet Bildiri)

  • Yayın Türü: Bildiri / Özet Bildiri
  • Basıldığı Şehir: İstanbul
  • Basıldığı Ülke: Türkiye
  • Sayfa Sayıları: ss.97
  • İstanbul Ticaret Üniversitesi Adresli: Evet

Özet

In this paper, we extend the Source-Environment-Response (SER) by (Muhammad et. al 2026) to QSER. QSER

is a physics-guided decomposition that separates an observed response R into a conservative source field S and

an environmental influence field E such that R = S − E. The source field evolves under purely conservative

dynamics, preserving perfect memory of initial conditions, while the environmental field starts from zero and

accumulates the entire history of dissipative and nonlinear interactions. Using a forced RLC circuit, we demonstrate

the Green’s function formulation showing that E(t) is precisely the convolution of the system’s memory

kernel with the dissipative source term, revealing the environment as a causal memory accumulator rather than

a passive energy sink. We extend the framework to the van der Pol oscillator, where all nonlinear complexity

is confined to E while S remains linear and conservative. The dissipation term DE = μ(1 − x2) ˙E2 can become

negative when |x| > 1, representing energy injection that allows the environmental energy EE to exceed

the source energy ES by a factor of approximately 6. This demonstrates that the environment can act as an active

energy source, not only as a sink. Four built-in validity tests; energy conservation in S, zero initial condition of

E, exact reconstruction, and infinite memory of S, provide self-validation absent in traditional approaches. The

QSER framework reveals that any measured quantity Q is not directly the source, but the difference between the

system’s pristine memory and the environment’s accumulated history, offering causal clarity, energy transparency,

and methodological flexibility across linear and nonlinear dissipative systems. All code is available open-source

at https://github.com/1030ahmad1030/Qtheory