We investigate the Belousov–Zhabotinsky (BZ) reaction in an attempt to establish a basis for computation using chemical oscillators coupled via inhibition. The system consists of BZ droplets suspended in oil. Interdrop coupling is governed by the non-polar communicator of inhibition, Br2. We consider a linear arrangement of three droplets to be a NOR gate, where the center droplet is the output and the other two are inputs. Oxidation spikes in the inputs, which we define to be TRUE, cause a delay in the next spike of the output, which we read to be FALSE. Conversely, when the inputs do not spike (FALSE) there is no delay in the output (TRUE), thus producing the behavior of a NOR gate. We are able to reliably produce NOR gates with this behavior in microfluidic experiment.

We consider a glassy system of interacting spins driven by continual switching amongst a finite set of nonuniform external fields. We find that the system evolves over time towards configurations that minimize the work absorbed from this external drive. The configurations which achieve this are specific to the details of the external fields used to drive the system, and therefore act effectively as a self-organized novelty-detector that embodies accurate predictions about the typical future of its external environment.

Diverse many-body systems, from soap bubbles to suspensions to polymers, learn and remember patterns in the drives that push them far from equilibrium. This learning may be leveraged for computation, memory, and engineering. Until now, many-body learning has been detected with thermodynamic properties, such as work absorption and strain. We progress beyond these macroscopic properties first defined for equilibrium contexts: We quantify statistical mechanical learning using representation learning, a machine-learning model in which information squeezes through a bottleneck. By calculating properties of the bottleneck, we measure four facets of many-body systems’ learning: classification ability, memory capacity, discrimination ability, and novelty detection. Numerical simulations of a classical spin glass illustrate our technique. This toolkit exposes self-organization that eludes detection by thermodynamic measures: Our toolkit more reliably and more precisely detects and quantifies learning by matter while providing a unifying framework for many-body learning.

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