Directed walks shape a universal square-root law of entropy production rate in nonreciprocal systems
Why complex systems always waste energy in predictable patterns
Systems with nonreciprocal interactions — where A influences B differently than B influences A — produce entropy (disorder and wasted energy) at rates that follow a universal mathematical pattern, regardless of how the system is organized. The researchers show that this square-root relationship emerges from the geometry of directed paths through the network, not from the system's detailed structure or how many components it has.
Understanding how biological and engineered networks waste energy matters for designing efficient systems — from neural circuits to chemical reactions to supply chains. This work reveals that the efficiency loss follows a predictable formula across radically different system types, which could help engineers set realistic performance targets and predict where to intervene to reduce waste.