Dresden 2026 – scientific programme
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SOE: Fachverband Physik sozio-ökonomischer Systeme
SOE 4: Poster Session
SOE 4.3: Poster
Monday, March 9, 2026, 18:00–21:00, P4
Realizable Circuit Complexity: Embedding Computation in Space-Time — •Benjamin Prada and Ankur Mali — University of South Florida, Tampa, FL
Parallel computation is typically modeled as a process carried out by abstract machines that ignore the constraints of physical reality. Although the evolution of real-world systems may be mapped to these abstractions, reverse translation is almost always impossible; most computations cannot be simulated in real-time by any device obeying finite propagation speed, bounded volume, or finite entropy. To remedy this discongruity between computational and physical theory, we introduce a framework of realizable circuits RCd that incorporates a d-dimensional spatial embedding directly into the computation model. The key is that information must cross geometric boundaries at a finite rate: fine-grained entropy flow through a (d−1)-dimensional boundary limits the number of independent bits that can be transformed or erased within a d-dimensional region. This yields physically motivated lower bounds on parallel depth and communication, connecting known theoretical and empirical results such as Landauer’s principle and Rent’s rule. Although the framework is general, we illustrate its usefulness by analyzing modern neural architectures (e.g., transformers and recurrent networks), whose parallel speedups are similarly constrained by entropy flux through bounded interfaces. The resulting theory offers a physics-aligned perspective on the fundamental limits of parallel computation, independent of any specific classical or quantum computing substrate.
Keywords: Energy; Quantum Mechanics; Thermodynamics; Conservation; Entropy