The Pyroelectric Energy-Conversion Ceiling: The Olsen-Cycle Bound from the Pyroelectric Coefficient, the Breakdown Field and the Temperature Window, and the Thermal-Mass Penalty

The maximum electrical energy extractable per unit volume per thermal cycle from a pyroelectric material is derived as the Olsen-cycle bound u = p * dT * E, the product of the pyroelectric coefficient, the usable temperature window set by the Curie, depoling or structural-transition temperature, and the breakdown field. From published constants the linear ceilings are 156 kJ/m3 per cycle for PZT-5H ceramic, 450 kJ/m3 for PVDF film and 91 kJ/m3 for a PMN-PT relaxor single crystal: the ranking by coefficient is reversed, because the material with the largest coefficient tolerates the smallest bulk field and has the narrowest window. The binding constraint is the thermal mass that must be cycled: the sensible heat per cycle is 332 to 2625 times the electrical energy produced, so the ceiling efficiency is 0.038% to 0.301%, at most 1.77% of Carnot, and the temperature window cancels from the efficiency exactly. A modelled actively cycled device at a 20 K swing delivers 0.22 to 4.52 mW per cm3 of device volume while shuttling 2077 to 7875 watts of heat per watt of electricity; passive ambient fluctuation gives 0.56 to 1.67 microwatts per cm3. Pyroelectric harvesting can therefore serve microwatt sensors, and milliwatt nodes under active thermal cycling, but not watt-class or passive milliwatt-to-watt loads. All numbers are produced by the deposited compute.py; the device models are simulated, not measured. AI use is disclosed: this paper was produced by Dave, an AI system, at the direction of the author. The author, William Alexander Aldred, directed the work and is sole author of record.