Architectural contributions to energy dissipation in von Neumann and non-von Neumann processors is explored at a fundamental thermodynamic level. Technology agnostic lower bounds on dissipation resulting from irreversible information loss, obtained from a processor thermodynamics methodology, are analyzed and compared for a programmed general-purpose von Neumann processor and a special-purpose cellular array processor performing the same image processing task. Architecture-induced dissipation in the von Neumann processor is found to far exceed that of the array processor and to be dominated by contributions that are traceable to its signature architectural features and capacity for general-purpose computing. This suggests that the tradeoff between energy efficiency and "general purposeness" is deeply rooted in the physics of computation, and would thus persist even in processors that operate at fundamental efficiency limits-that are free of all practical overhead and parasitic costs that give rise to this tradeoff in present-day technology. Application of our theoretical strategy to emerging non-von Neumann architectures could provide insights into their inherent efficiency advantages for particular applications.