batteryVoltage
plain-language theorem explainer
Battery voltage is expressed as the chemical potential difference between anode and cathode divided by elementary charge. Recognition Science researchers cite this when treating electrochemical cells as J-cost gradient devices that drive current via particle flow to lower total cost. The definition is a direct string assignment that links voltage to the underlying recognition mechanism without invoking lemmas or computation.
Claim. $V = (μ̃_anode - μ̃_cathode)/e$, where the chemical potential difference drives current and the battery functions as a J-cost gradient device.
background
The module derives chemical potential from J-cost gradients. Chemical potential μ equals the partial derivative of free energy F with respect to particle number N at fixed T and V, equivalently the gradient of total J-cost with respect to N. Particles flow from high to low μ to minimize overall J-cost, and μ determines ledger occupation in the recognition framework. Upstream results supply J_total as the sum of mass and light contributions for stellar configurations, the cost of a recognition event as the J-cost of its state, and the inflaton potential as J-cost evaluated at a dimensionless displacement from the reference rung.
proof idea
Direct definition that assigns an explanatory string. No lemmas are applied; the body is a literal string that summarizes the RS view of voltage as a chemical-potential difference.
why it matters
The definition anchors the battery example inside the chemical-potential module and illustrates how J-cost gradients produce observable voltage. It aligns with the module target of deriving μ from recognition costs and with the broader forcing chain that yields spatial dimensions and the Recognition Composition Law. No downstream theorems are recorded, indicating the declaration functions as a conceptual summary rather than a computational primitive.
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