VacuumPower
plain-language theorem explainer
The VacuumPower definition supplies the scaling relation for power output in an entropic vacuum pump as the product of operating frequency and metric stiffness gradient. Researchers modeling metric engines or entropic generators within Recognition Science would reference this relation when balancing input pulses against ordered vacuum output. The definition is realized by a direct one-line product expression.
Claim. The vacuum power output is given by $P(f, sigma_{grad}) = f · sigma_{grad}$, where $f$ is the frequency of the metric engine and $sigma_{grad}$ is the gradient of its metric stiffness.
background
The module formalizes thermodynamics for a Metric Engine acting as a generator. Standard thermodynamics converts work to heat with entropy increase; RS thermodynamics converts ordering of vacuum fluctuations to heat absorption with entropy decrease. The device functions as a metric Maxwell's demon that sorts fluctuations to lower J-cost, with the cost paid by absorbing thermal entropy from the environment. Energy balance takes an initial pulse plus environmental heat as input and yields ordered vacuum plus EMF as output, producing net gain relative to stored fuel but unity relative to the total environment. The definition rests on the upstream theorem from PrimitiveDistinction that extracts four structural conditions plus three definitional facts from seven independent axioms.
proof idea
This definition is implemented as a direct one-line expression that multiplies the frequency parameter by the sigma gradient parameter.
why it matters
This definition supplies the quantitative scaling law for the vacuum pump mechanism inside the Energy module and supports the entropic pumping hypothesis that reverses classical entropy flow. It connects to the Recognition framework by quantifying how metric ordering yields usable output, consistent with the J-cost reduction described in the module. No downstream theorems are listed, yet the definition pairs with sibling entries such as EntropicCooling and RunawaySignature to sketch full device signatures.
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