This is a framework that closes the line from atomic-circuit analogy to biology at the DNA level: it establishes the double helix as a “double-stranded conduction line”, base pairs as “paired diode-capacitor cells”, the sugar-phosphate backbone as a “periodic RC ladder”, protein interactions as “control transistors”, and replication/transcription as “state machine switching networks”.
Euler’s identity establishes the equivalence of complex exponents with trigonometric functions by combining fundamental constants such as e, i, and π:
Based on the circuit analogy I’ve created, let’s now map gases and gas laws to circuit topology using the same logic. This way, we can express the behavior of gases in the periodic table using electrical parameters.
Entropic impedance physics is defined as a new physical paradigm that combines energy transport modes, geometric curvatures and phase conformations in a single framework. This approach offers an interdisciplinary field theory.
Physical expression: In a pipeline, the flow entering is equal to the flow leaving. Analogical expression: – Flow (Q) ↔ Current (I) – “Current in = current out” → Same structure as Kirchhoff’s current law.
Proposition: “The potential difference resulting from resistance is weight.” Circuit analogy mapping: – Color space → Voltage source (𝑉s) – Entropic impedance → Resistance (𝑅) – Information/energy flow → Current (𝐼) – Potential difference → Voltage drop (Δ𝑉) – Weight → Spatially scaled equivalent of voltage drop (Δ𝑉/ℓ) – Mass → Weight divided by 𝑔
Phase–duality algebra is a unique structure that combines the geometric, algebraic and physical properties of trigonometric functions (sin, cos, sec, csc, tan, cot) and covers both circular and hyperbolic rotations. This algebra is reinterpreted within the framework of Clifford algebra and Lie groups, providing a strong basis for both mathematical consistency and physical modelling.
Maxwell’s analogy is a framework built on four fundamental equations that show that electric and magnetic fields are interconnected. Thanks to this analogy, it was demonstrated that light is actually an electromagnetic wave, and strong analogies were established between electrical circuits and wave behavior.
This article describes Quantum Circuit Topology, an original approach that combines quantum particle physics and circuit physics. The main starting point of the study is the idea that the laws of nature repeat in the same way at different scales. Particles such as quarks, gluons, electrons and neutrinos are interpreted as circuit elements; Quantum concepts such as entanglement, superposition, spin and color field are modeled in circuit-topological form. This analogical approach intuitively offers a new paradigm and has the potential to evolve into a scientific discipline with future experimental validation.
In classical quantum mechanics, the uncertainty principle is considered an absolute and immutable law of nature. The uncertainty product of complementary quantities such as phase and current cannot fall below a certain lower limit under any circumstances. In Ümit Arslan’s circuit-topological model, this approach changes radically. The uncertainty principle is not the necessary limit of nature; It is redefined as the measurement result based on the architecture.