Elementary Characteristics and Energy Transport in Physical Reservoir Computing

Abstract

Physical reservoir computing (PRC) exploits the high-dimensional dynamics of physical systems to process information efficiently. In contrast to digital computation, where logic is explicitly programmed, PRC leverages the inherent energy redistribution and dissipation of dynamical systems to provide memory and nonlinearity. This paper develops a perspective on the elementary characteristics of physical reservoirs, emphasising energy transport as the unifying principle. We examine how the echo state property (ESP) emerges through dissipation, distinguishing reservoirs from mere input channels, and demonstrate how ESP provides the foundation for reproducibility, fading memory, and computational expressiveness. Following the development history of physics, we move from classical physics, including classical mechanics and electromagnetism, to quantum mechanics, for a brief overview of PRC across different physical branches. Classical mechanical systems are presented as canonical reservoirs, with mass–spring–damper models capturing the interplay between inertia, elasticity, and damping as a computational substrate. We then discuss optical reservoir computing, where nonlinearity and time-delay memory in photonic devices enable high-speed processing. Finally, we consider quantum mechanical systems, where the quantum dynamics and decoherence govern energy transport, offering new opportunities for parallel computation. Across these domains, we show that engineering reservoirs amounts to co-designing energy flows, dissipation, and expressiveness under thermodynamic constraints. This perspective positions energy transport and ESP as fundamental to understanding and designing PRC systems.