Thermodynamic control of patent tokenization for sustainable development

Background Patent tokenization converts intellectual property (IP) into tradable digital units. Pilots on IPwe, IBM, and Ocean Protocol have processed <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="m1"> <mml:mrow> <mml:mo>&gt;</mml:mo> </mml:mrow> </mml:math> 1,500 assets ( <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="m2"> <mml:mrow> <mml:mo>≈</mml:mo> </mml:mrow> </mml:math> $62 million since 2019). In practice, schedules are often fixed and pricing simplified; risk preferences are typically ignored—costing value in volatile settings relevant to the SDGs. Methods We cast patent tokenization as risk-sensitive control and linked economic risk aversion to inverse temperature. With the exponential transform <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="m3"> <mml:mrow> <mml:mi mathvariant="normal">Φ</mml:mi> <mml:mo>=</mml:mo> <mml:msup> <mml:mrow> <mml:mi>e</mml:mi> </mml:mrow> <mml:mrow> <mml:mo>−</mml:mo> <mml:mi>γ</mml:mi> <mml:mi>V</mml:mi> </mml:mrow> </mml:msup> </mml:mrow> </mml:math> , the risk-sensitive Hamilton–Jacobi–Bellman (HJB) linearizes for fixed controls; the optimal policy is a pointwise threshold (bang–bang or smoothly regularized). This preserves tractability and enables millisecond solves. Results From 45 tokenization trajectories (12 held out), we estimate <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="m4"> <mml:mrow> <mml:mi>γ</mml:mi> <mml:mo>=</mml:mo> <mml:mn>2.1</mml:mn> <mml:mo>±</mml:mo> <mml:mn>0.38</mml:mn> </mml:mrow> </mml:math> (95% CI), while a composite objective <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="m5"> <mml:mrow> <mml:mi>F</mml:mi> <mml:mrow> <mml:mo stretchy="false">(</mml:mo> <mml:mrow> <mml:mi>γ</mml:mi> </mml:mrow> <mml:mo stretchy="false">)</mml:mo> </mml:mrow> </mml:mrow> </mml:math> calibrated to equity-like orders peaks at <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="m6"> <mml:mrow> <mml:msup> <mml:mrow> <mml:mi>γ</mml:mi> </mml:mrow> <mml:mrow> <mml:mo>*</mml:mo> </mml:mrow> </mml:msup> <mml:mo>≈</mml:mo> <mml:mn>3.02</mml:mn> </mml:mrow> </mml:math> ([2.9,3.2]). Monte Carlo <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="m7"> <mml:mrow> <mml:mo stretchy="false">(</mml:mo> <mml:mrow> <mml:mi>n</mml:mi> <mml:mo>=</mml:mo> <mml:mn>10,000</mml:mn> </mml:mrow> <mml:mo stretchy="false">)</mml:mo> </mml:mrow> </mml:math> shows a <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="m8"> <mml:mrow> <mml:mo>≈</mml:mo> </mml:mrow> </mml:math> 76% downside reduction and 92% success rate under ledger-based schedules. Solver latency drops by <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="m9"> <mml:mrow> <mml:mo>∼</mml:mo> <mml:mn>850</mml:mn> <mml:mo>×</mml:mo> </mml:mrow> </mml:math> (40 s <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="m10"> <mml:mrow> <mml:mo>→</mml:mo> </mml:mrow> </mml:math> 47 ms). Conclusion The thermodynamic lens explains why practice <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="m11"> <mml:mrow> <mml:mo stretchy="false">(</mml:mo> <mml:mrow> <mml:mi>γ</mml:mi> <mml:mo>≈</mml:mo> <mml:mn>2.1</mml:mn> </mml:mrow> <mml:mo stretchy="false">)</mml:mo> </mml:mrow> </mml:math> deviates from the theoretical benchmark <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="m12"> <mml:mrow> <mml:mo stretchy="false">(</mml:mo> <mml:mrow> <mml:msup> <mml:mrow> <mml:mi>γ</mml:mi> </mml:mrow> <mml:mrow> <mml:mo>*</mml:mo> </mml:mrow> </mml:msup> <mml:mo>≈</mml:mo> <mml:mn>3.0</mml:mn> </mml:mrow> <mml:mo stretchy="false">)</mml:mo> </mml:mrow> </mml:math> in our calibration: actors appear to trade maximal efficiency for robustness. The framework stabilizes revenues, drives fees to negligible levels, and supports SDG-aligned innovation finance by lowering the cost of access and adaptation under uncertainty.