Physical systems are increasingly seen as an alternative to digital computers, but there is a lack of principles for estimating their computational potential in advance. Active matter, which continuously consumes energy and produces entropy, serves as a convenient testbed. The work sits at the intersection of nonequilibrium thermodynamics and reservoir computing, alongside studies of chaos, noise, and self-organization. Related papers examine how to measure chaos without knowing the system's rules, how to predict noisy chaos, and how quantum chaos gives rise to thermal equilibrium, but the connection between entropy and computational power remained unexplored.
The authors simulated a swarm of 200 particles with repulsive forces, velocity alignment, attraction to home, and speed control. An external signal was fed through a driver particle whose trajectory was set by the chaotic Lorenz-63 system. The entropy production of the system was calculated via phase-space contraction using the generalized Liouville equation and a Monte Carlo method, while heat flow into the environment was computed through the work of nonconservative forces. Reservoir performance was assessed by the Pearson correlation between the predicted and true driver coordinate. They scanned two parameters: the strength of the speed controller and the target speed of the particles, as well as the strength and radius of the driver's repulsion.
In a system without a driver, heat flow is minimal in a regime close to critical damping, and when the driver is switched on, this regime yields the largest increase in heat flow and driver work. Reservoir performance peaks (correlation up to 0.97) precisely in this regime. The relative difference between the driven and undriven entropy of the system reaches 40, and for heat flow it is about 6000, indicating a strong influence of the driver. Spearman correlations between performance and driver work, as well as relative entropy differences, exceed 0.8, whereas absolute entropy values correlate more weakly. The coefficient of variation of entropy and heat flow correlates negatively with performance, meaning that better reservoirs are more robust to initial conditions.
The work shows that entropy production is not a universal scalar indicator of computational ability, but its diagnostic value emerges when contributions are separated: phase-space contraction, dissipation into the environment, and changes caused by the external signal. Unlike related studies that treated entropy as a marker of nonequilibrium or linked it to phase transitions, this work establishes for the first time a quantitative connection between thermodynamic response and reservoir performance. The method for estimating entropy via the generalized Liouville equation is applicable to any system of ordinary differential equations, which expands the toolkit for analyzing physical computation.
It would be promising to study thermodynamically consistent couplings to a thermal bath in order to obtain a complete entropy balance and refine the interpretation of dissipation. It is also important to link entropy production to information measures such as memory or information transfer, and to test whether entropy can serve as a universal screening indicator for different classes of reservoirs.
The results could aid the development of physical reservoir computers based on active matter, photonic, or spin systems, allowing suitable regimes to be selected without costly training.
Test the predictive power of entropy metrics on other reservoirs and with other input signals, and develop experimental methods for measuring entropy production in real active systems.
The work directly addresses the unsolved problem of the connection between thermodynamic cost and computational ability in nonequilibrium systems, as well as the question of which observables can serve as reliable indicators of performance without training.
The reservoir's maximum performance is achieved in a regime where heat flow into the environment is minimal in the absence of a signal, but increases thousands of times when the signal is applied.
The idea of using a swarm of particles for computation echoes the concept of 'computing matter' from Stanisław Lem's novel The Invincible, where a collective of microscopic machines processes information.