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Biomolecules stochastically occupy different possible configurations with probabilities given by non-equilibrium steady-state distributions. These distributions are determined by the transition rate constants between different configurations. Changing these biochemical parameters (inputs) alters the resulting distributions (outputs), and thus constitutes a form of computation. The information-theoretic advantage of performing computations using non-equilibrium distributions, which require a thermodynamic driving force and thus continual energy expenditure to maintain, is unclear. Here we show how much driving can change probability distributions beyond what is possible at equilibrium. First, we establish a tight limit on how much the driving force can change the probability of observing any configuration of an arbitrary molecular system. We then derive a concise expression relating the driving force to the maximum information gain -- the change in the full probability distribution over configurations -- in any computation, showing how small input changes can exponentially alter outputs. Finally, we numerically show that synthetic systems and Ras signaling can closely approach this bound, illustrating the necessity of energy expenditure to enable the computational capabilities observed in nature.

Living systems efficiently use chemical fuel to do work, process information, and assemble patterns despite thermal noise. Whether high efficiency arises from general principles or specific fine-tuning is unknown. Here, applying a recent mapping from nonequilibrium systems to battery-resistor circuits, I derive an analytic expression for the efficiency of any dissipative molecular machine driven by one or a series of chemical potential differences. This expression disentangles the chemical potential from the machine's details, whose effect on the efficiency is fully specified by a constant called the load resistance. The efficiency passes through a switch-like inflection point if the balance between chemical potential and load resistance exceeds thermal noise. Therefore, dissipative chemical engines qualitatively differ from heat engines, which lack threshold behavior. This explains all-or-none dynein stepping with increasing ATP concentration observed in single-molecule experiments. These results indicate that biomolecular energy transduction is efficient not because of idosyncratic optimization of the biomolecules themselves, but rather because the concentration of chemical fuel is kept above a threshold level within cells.

In living systems, collective molecular behavior is driven by thermodynamic forces in the form of chemical gradients. Leveraging recent advances in the field of nonequilibrium physics, I show that increasing the thermodynamic force alone can induce qualitatively new behavior. To demonstrate this principle, general equations governing kinetic proofreading and microtubule assembly are derived. These equations show that new capabilities, including catalytic regulation of steady-state behavior and exponential enhancement of molecular discrimination, are only possible if the system is driven sufficiently far from equilibrium, and can emerge sharply at a threshold force. Regardless of design parameters, these results reveal that the thermodynamic force sets fundamental performance limits on tuning sensitivity, error, and waste. Experimental data show that these biomolecular processes operate at the limits allowed by theory.

Human reasoning can distill principles from observed patterns and generalize them to explain and solve novel problems. The most powerful artificial intelligence systems lack explainability and symbolic reasoning ability, and have therefore not achieved supremacy in domains requiring human understanding, such as science or common sense reasoning. Here we introduce deep distilling, a machine learning method that learns patterns from data using explainable deep learning and then condenses it into concise, executable computer code. The code, which can contain loops, nested logical statements, and useful intermediate variables, is equivalent to the neural network but is generally orders of magnitude more compact and human-comprehensible. On a diverse set of problems involving arithmetic, computer vision, and optimization, we show that deep distilling generates concise code that generalizes out-of-distribution to solve problems orders-of-magnitude larger and more complex than the training data. For problems with a known ground-truth rule set, deep distilling discovers the rule set exactly with scalable guarantees. For problems that are ambiguous or computationally intractable, the distilled rules are similar to existing human-derived algorithms and perform at par or better. Our approach demonstrates that unassisted machine intelligence can build generalizable and intuitive rules explaining patterns in large datasets that would otherwise overwhelm human reasoning.

How perception and reasoning arise from neuronal network activity is poorly understood. This is reflected in the fundamental limitations of connectionist artificial intelligence, typified by deep neural networks trained via gradient-based optimization. Despite success on many tasks, such networks remain unexplainable black boxes incapable of symbolic reasoning and concept generalization. Here we show that a simple set of biologically consistent organizing principles confer these capabilities to neuronal networks. To demonstrate, we implement these principles in a novel machine learning algorithm, based on concept construction instead of optimization, to design deep neural networks that reason with explainable neuron activity. On a range of tasks including NP-hard problems, their reasoning capabilities grant additional cognitive functions, like deliberating through self-analysis, tolerating adversarial attacks, and learning transferable rules from simple examples to solve problems of unencountered complexity. The networks also naturally display properties of biological nervous systems inherently absent in current deep neural networks, including sparsity, modularity, and both distributed and localized firing patterns. Because they do not sacrifice performance, compactness, or training time on standard learning tasks, these networks provide a new black-box-free approach to artificial intelligence. They likewise serve as a quantitative framework to understand the emergence of cognition from neuronal networks.

The Boltzmann distribution predicts the collective behavior of systems at thermodynamic equilibrium as a function of their constituent parts. Yet most systems in nature are not at equilibrium, and a unified theory of their behavior does not currently exist. Here, I show that the Boltzmann distribution is a special case of a general distribution that governs all stochastic systems, even if far from equilibrium. The generalized Boltzmann distribution is explained as an analog of the voltage equation in electronics, where resistors, batteries, node voltages, and path currents correspond to equilibrium rate constants, driven rate constants, probabilities, and probability flows, respectively. The general distribution recapitulates known properties of weakly driven systems and enables new closed-form solutions for strongly-driven systems. These solutions provide insight into fundamental limits on system performance, and experimental data show that living systems can operate at those limits. The formal mapping between non-equilibrium systems and electronic circuits may provide a unified framework to simplify, understand, and ultimately control the behavior of complex non-equilibrium systems., Comment: Added additional clarifying examples, and more detailed derivations of the results as supplementary information