The thermodynamic efficiency of coupled chaotic dissipative structures

TL;DR

This paper extends the thermodynamic efficiency analysis of chaotic dissipative structures, specifically coupled Lorenz waterwheels, introducing new coupling types and deriving efficiency formulas with confirmed numerical behaviors.

Contribution

It introduces two canonical couplings for dissipative structures, proves association laws for efficiency reduction, and applies these to coupled Lorenz waterwheels with validated simulations.

Findings

Series coupling increases thermodynamic efficiency.

Parallel coupling averages efficiency and boosts energy flow.

Synchronization generally benefits efficiency.

Abstract

Dissipative structures are open dynamical systems that sustain coherent macroscopic organization by continuously exchanging energy and matter with their environment and generating entropy. A recent thermodynamic analysis of the paradigmatic Malkus--Lorenz waterwheel interpreted the Lorenz system as an engine, deriving an exact formula for its thermodynamic efficiency, and showing that efficiency tends to increase as the system is driven far from equilibrium while displaying sharp drops near the Hopf subcritical bifurcation to chaos. Here, we extend that single-engine framework to coupled dissipative structures. We introduce two canonical couplings -- master-slave coupling (series) and symmetric diffusive coupling (parallel) -- and prove two fundamental association laws allowing us to reduce the composite systems to an equivalent engine with a specified efficiency. We then apply these abstract results to coupled Lorenz waterwheels, deriving efficiency formulas consistent with the underlying power balance. We perform numerical simulations confirming that (a) series coupling induces an increase in thermodynamic efficiency, (b) parallel coupling averages the efficiency of engines and increases total energy flow, (c) synchronization is typically neutral or beneficial for efficiency except in narrow parameter regions, and (d) coupling modifies the curvature of entropy-generation trends. Our theorems suggest a mathematically rigorous and transparent route to define and compute thermodynamic efficiency for generalized flow networks, with potential application to complex systems energetics.