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Ken A. Dill

Publications and source records attributed to Ken A. Dill.

At least 19 recordsLinked to original sources
arXiv2026

Nonequilibrium Theory for Molecular Machine Design

Modeling the dynamical flows on networks of biomolecular machines often entails computing node populations and edge fluxes with Master Equations and correlating machine performance with entropy production. But this alone is not sufficient for design, optimization and evolution because it doesn't treat cost-benefit tradeoffs, or small-system misflows (backsteps, futile cycles, ineffective actions), or differential properties for flow design. Here we develop CFT Design, based on the recently developed Caliber Force Theory (CFT). We apply it to: designing faster molecular motors through ``traffic control''; optimizing speed, energy, and accuracy in kinetic proofreaders; and designing better enzyme inhibitors. CFT Design provides a general framework for optimizing nonequilibrium flow networks.

cond-mat.stat-mech↗
arXiv2026

Fluctuation-Response Design Rules for Nonequilibrium Flows

Biological machines like molecular motors and enzymes operate in dynamic cycles representable as stochastic flows on networks. Current stochastic dynamics describes such flows on fixed networks. Here, we develop a scalable approach to network design in which local transition rates can be systematically varied to achieve global dynamical objectives. It is based on the fluctuation-response duality in the recent Caliber Force Theory -- a path-entropy variational formalism for nonequilibria. This approach scales efficiently with network complexity and gives new insights, for example revealing the transition from timing- to branching-dominated fluctuations in a kinesin motor model.

cond-mat.stat-mech↗
arXiv2026

Nonequilibrium Theory for Adaptive Systems in Varying Environments

Biological organisms are adaptive, able to function in unpredictably changing environments. Drawing on recent nonequilibrium physics, we show that in adaptation, fitness has two components parameterized by observable coordinates: a static Generalism component characterized by state distributions, and a dynamic Tracking component sustained by nonequilibrium fluxes. Our findings: (1) General Theory: We prove that tracking gain scales strictly with environmental variability and switching time-scales; near-static or fast-switching environments are not worth tracking. (2) Optimal Strategies: We explain optimal bet-hedging and phenotypic memory as the interplay between these components. (3) Control: We demonstrate, with an example, how to suppress pathogens by independently attacking their Generalism robustness (via environmental time fractions) and Tracking capabilities (via environmental switching speed). This work provides a physical framework for understanding and controlling adaptivity.

cond-mat.stat-mech↗
arXiv2025

A Principled Basis for Nonequilibrium Network Flows

The great power of EQuilibrium (EQ) statistical physics comes from its principled foundations: its First Law (conservation), Second Law (variational tendency principle), and its Legendre Transforms from observables $(U, V, N)$ to their driving forces $(T, p, μ)$. Here, we generalize this structure to Non-EQuilibria (NEQ) in \textit{Caliber Force Theory} (CFT), replacing state entropies with path entropies; and $(U, V, N)$ with dynamic observables (node probabilities, edge traffics, and cycle fluxes). CFT derives dynamical forces and a complete set of conjugate relations: (i) It yields generalized Maxwell-Onsager relations, applicable far from equilibrium; (ii) It constructs dynamical models from mixed force-observable constraints; and (iii) It reveals new relationships -- including an ``equal-traffic'' rule for optimizing molecular motors, and a ``third Kirchhoff's law'' of stochastic transport -- and can resolve some dynamical paradoxes.

cond-mat.stat-mech↗
arXiv2025

Statistical mechanical theory of liquid water

Water is an unusual liquid. Its thermophysical properties are non-monotonic with temperature T and pressure p. It's not been known how water's behaviors are encoded in its molecules. We give a statistical physics model, Cage Water, which assumes three bonding states: van der Waals, pairwise hydrogen bonding, and multi-body cooperative caging hydrogen bonds. The model is analytical, so very fast to compute, yet it gives excellent agreement with extensive pT experiments. Through readily interpretable substates, Cage Water explains water's liquid anomalies -- including its controversial liquid-liquid supercooling transition -- as simple switchovers among the three bonding types.

cond-mat.stat-mech↗
arXiv2025

Deriving the Forces of Nonequilibria from Two Laws

Non-EQuilibrium (NEQ) statistical physics has not had the same general foundation as that of EQuilibrium (EQ) statistical physics, where forces are derived from potentials such as $1/T = \partial S/\partial U$, and from which other key mathematical relations follow. Here, we show how general NEQ principles can be derived from two corresponding laws. Maximizing path entropy replaces maximizing state entropy. Whereas EQ can entail observables $(U, V, N)$, dynamics has (node populations, edge traffic, cycle flux). We derive forces of NEQ, fluctuation-susceptibility equalities, Maxwell-Onsager-like symmetry relations, and we generalize to ``cost-benefit'' relations beyond just work and heat dissipation.

cond-mat.stat-mech↗
arXiv2023

The prebiotic emergence of biological evolution

The origin of life must have been preceded by Darwin-like evolutionary dynamics that could propagate it. How did that adaptive dynamics arise? And from what prebiotic molecules? Using evolutionary invasion analysis, we develop a universal framework for describing any origin story for evolutionary dynamics. We find that cooperative autocatalysts, i.e. autocatalysts whose per-unit reproductive rate grows as their population increases, have the special property of being able to cross a barrier that separates their initial degradation-dominated state from a growth-dominated state with evolutionary dynamics. For some model parameters, this leap to persistent propagation is likely, not rare. We apply this analysis to the Foldcat Mechanism, wherein peptides fold and help catalyze the elongation of each other. Foldcats are found to have cooperative autocatalysis and be capable of emergent evolutionary dynamics.

q-bio.PE↗
arXiv2023

The foundations of statistical physics: entropy, irreversibility, and inference

Statistical physics aims to describe properties of macroscale systems in terms of distributions of their microscale agents. Its central tool is the maximization of entropy, a variational principle. We review the history of this principle, first considered as a law of nature, more recently as a procedure for inference in model-making. And while equilibria (EQ) have long been grounded in the principle of Maximum Entropy (MaxEnt), until recently no equally foundational generative principle has been known for non-equilibria (NEQ). We review evidence that the variational principle for NEQ is Maximum Caliber. It entails maximizing \textit{path entropies}, not \textit{state entropies}. We also describe the role of entropy in characterizing irreversibility, and describe the relationship between MaxCal and other prominent approaches to NEQ physics, including Stochastic Thermodynamics (ST), Large Deviations Theory (LDT), Macroscopic Fluctuation Theory (MFT), and non-extensive entropies.

cond-mat.stat-mech↗
arXiv2022

Non-Equilibrium Statistical Physics Beyond the Ideal Heat Bath Approximation

Important models of nonequilibrium statistical physics (NESP) are limited by a commonly used, but often unrecognized, near-equilibrium approximation. Fokker-Planck and Langevin equations, the Einstein and random-flight diffusion models, and the Schnakenberg model of biochemical networks suppose that fluctuations are due to an ideal equilibrium bath. But far from equilibrium, this perfect bath concept does not hold. A more principled approach should derive the rate fluctuations from an underlying dynamical model, rather than assuming a particular form. Here, using Maximum Caliber as the underlying principle, we derive corrections for NESP processes in an imperfect - but more realistic - environment, corrections which become particularly important for a system driven strongly away from equilibrium. Beyond characterizing a heat bath by the single equilibrium property of its temperature, the bath's speed and size must also be used to characterize the bath's ability to handle fast or large fluctuations.

cond-mat.stat-mech↗
arXiv2020

Inferring a network from dynamical signals at its nodes

We give an approximate solution to the difficult inverse problem of inferring the topology of an unknown network from given time-dependent signals at the nodes. For example, we measure signals from individual neurons in the brain, and infer how they are inter-connected. We use Maximum Caliber as an inference principle. The combinatorial challenge of high-dimensional data is handled using two different approximations to the pairwise couplings. We show two proofs of principle: in a nonlinear genetic toggle switch circuit, and in a toy neural network.

physics.bio-ph↗
arXiv2017

Maximum Caliber: a general variational principle for dynamical systems

We review here {\it Maximum Caliber} (Max Cal), a general variational principle for inferring distributions of paths in dynamical processes and networks. Max Cal is to dynamical trajectories what the principle of {\it Maximum Entropy} (Max Ent) is to equilibrium states or stationary populations. In Max Cal, you maximize a path entropy over all possible pathways, subject to dynamical constraints, in order to predict relative path weights. Many well-known relationships of Non-Equilibrium Statistical Physics -- such as the Green-Kubo fluctuation-dissipation relations, Onsager's reciprocal relations, and Prigogine's Minimum Entropy Production -- are limited to near-equilibrium processes. Max Cal is more general. While it can readily derive these results under those limits, Max Cal is also applicable far from equilibrium. We give recent examples of MaxCal as a method of inference about trajectory distributions from limited data, finding reaction coordinates in bio-molecular simulations, and modeling the complex dynamics of non-thermal systems such as gene regulatory networks or the collective firing of neurons. We also survey its basis in principle, and some limitations.

cond-mat.stat-mech↗
arXiv2017

Caliber Corrected Markov Modeling (C2M2): Correcting Equilibrium Markov models

Rate processes are often modeled using Markov-State Models (MSM). Suppose you know a prior MSM, and then learn that your prediction of some particular observable rate is wrong. What is the best way to correct the whole MSM? For example, molecular dynamics simulations of protein folding may sample many microstates, possibly giving correct pathways through them, while also giving the wrong overall folding rate, when compared to experiment. Here, we describe Caliber Corrected Markov Modeling (C2M2): an approach based on the principle of maximum entropy for updating a Markov model by imposing state- and trajectory- based constraints. We show that such corrections are equivalent to asserting position-dependent diffusion coefficients in continuous-time continuous-space Markov processes modeled by a Smoluchowski equation. We derive the functional form of the diffusion coefficient explicitly in terms of the trajectory-based constraints. We illustrate with examples of 2D particle diffusion and an overdamped harmonic oscillator.

cond-mat.stat-mech↗
arXiv2017

Citation histories of papers: sometimes the rich get richer, sometimes they don't

We describe a simple model of how a publication's citations change over time, based on pure-birth stochastic processes with a linear cumulative advantage effect. The model is applied to citation data from the Physical Review corpus provided by APS. Our model reveals that papers fall into three different clusters: papers that have rapid initial citations and ultimately high impact (fast-hi), fast to rise but quick to plateau (fast-flat), or late bloomers (slow-late), which may either never achieve many citations, or do so many years after publication. In "fast-hi" and "slow-late", there is a rich-get-richer effect: papers that have many citations accumulate additional citations more rapidly while the "fast-flat" papers do not display this effect. We conclude by showing that only a few years of post-publication statistics are needed to identify high impact ("fast-hi") papers.

cs.DL↗
arXiv2015

Maximum caliber is a general variational principle for nonequilibrium statistical mechanics

There has been interest in finding a general variational principle for non-equilibrium statistical mechanics. We give evidence that Maximum Caliber (Max Cal) is such a principle. Max Cal, a variant of Maximum Entropy, predicts dynamical distribution functions by maximizing a path entropy subject to dynamical constraints, such as average fluxes. We first show that Max Cal leads to standard near-equilibrium results -including the Green-Kubo relations, Onsager's reciprocal relations of coupled flows, and Prigogine's principle of minimum entropy production -in a way that is particularly simple. More importantly, because Max Cal does not require any notion of 'local equilibrium', or any notion of entropy dissipation, or even any restriction to material physics, it is more general than many traditional approaches. We develop some generalizations of the Onsager and Prigogine results that apply arbitrarily far from equilibrium. Max Cal is not limited to materials and fluids; it also applies, for example, to flows and trafficking on networks more broadly.

cond-mat.stat-mech↗
arXiv2015

A maximum entropy framework for non-exponential distributions

Probability distributions having power-law tails are observed in a broad range of social, economic, and biological systems. We describe here a potentially useful common framework. We derive distribution functions $\{p_k\}$ for situations in which a `joiner particle' $k$ pays some form of price to enter a `community' of size $k-1$, where costs are subject to economies-of-scale (EOS). Maximizing the Boltzmann-Gibbs-Shannon entropy subject to this energy-like constraint predicts a distribution having a power-law tail; it reduces to the Boltzmann distribution in the absence of EOS. We show that the predicted function gives excellent fits to 13 different distribution functions, ranging from friendship links in social networks, to protein-protein interactions, to the severity of terrorist attacks. This approach may give useful insights into when to expect power-law distributions in the natural and social sciences.

physics.soc-ph↗
arXiv2015

Simulated evolution of protein-protein interaction networks with realistic topology

We model the evolution of eukaryotic protein-protein interaction (PPI) networks. In our model, PPI networks evolve by two known biological mechanisms: (1) Gene duplication, which is followed by rapid diversification of duplicate interactions. (2) Neofunctionalization, in which a mutation leads to a new interaction with some other protein. Since many interactions are due to simple surface compatibility, we hypothesize there is an increased likelihood of interacting with other proteins in the target protein's neighborhood. We find good agreement of the model on 10 different network properties compared to high-confidence experimental PPI networks in yeast, fruit flies, and humans. Key findings are: (1) PPI networks evolve modular structures, with no need to invoke particular selection pressures. (2) Proteins in cells have on average about 6 degrees of separation, similar to some social networks, such as human-communication and actor networks. (3) Unlike social networks, which have a shrinking diameter (degree of maximum separation) over time, PPI networks are predicted to grow in diameter. (4) The model indicates that evolutionarily old proteins should have higher connectivities and be more centrally embedded in their networks. This suggests a way in which present-day proteomics data could provide insights into biological evolution.

q-bio.MN↗
arXiv2014

Inferring microscopic kinetics of a Markov process using maximum caliber

We present a principled approach for estimating the matrix of microscopic rates among states of a Markov process, given only its stationary state population distribution and a single average global kinetic observable. We adapt Maximum Caliber, a variational principle in which a path entropy is maximized over the distribution of all the possible trajectories, subject to basic kinetic constraints and some average dynamical observables. We show that this approach leads, under appropriate conditions, to the continuous-time master equation and a Smoluchowski-like equation that is valid for both equilibrium and non-equilibrium stationary states. We illustrate the method by computing the solvation dynamics of water molecules from molecular dynamics trajectories.

cond-mat.stat-mech↗