arXiv subjects

Ying-Jen Yang

Publications and source records attributed to Ying-Jen Yang.

15 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↗

arXiv2025

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↗

arXiv2024

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 $(T, p, \mu)$. 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↗

arXiv2024

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↗

arXiv2024

Maximum Caliber Infers Effective Coupling and Response from Spiking Networks

The characterization of network and biophysical properties from neural spiking activity is an important goal in neuroscience. A framework that provides unbiased inference on causal synaptic interaction and single neural properties has been missing. Here we applied the stochastic dynamics extension of Maximum Entropy -- the Maximum Caliber Principle -- to infer the transition rates of network states. Effective synaptic coupling strength and neuronal response functions for various network motifs can then be computed. The inferred minimal model also enables leading-order reconstruction of inter-spike interval distribution. Our method is tested with numerical simulated spiking networks and applied to data from salamander retina.

q-bio.NC↗

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

Statistical Uncertainty Principle in Stochastic Dynamics

Maximum entropy principle identifies forces conjugated to observables and the thermodynamic relations between them, independent upon their underlying mechanistic details. For data about state distributions or transition statistics, the principle can be derived from limit theorems of infinite data sampling. This derivation reveals its empirical origin and clarify the meaning of applying it to large but finite data. We derive an uncertainty principle for the statistical variations of the observables and the inferred forces. We use a toy model for molecular motor as an example.

cond-mat.stat-mech↗

arXiv2021

Duality Symmetry, Two Entropy Functions, and an Eigenvalue Problem in Gibbs' Theory

We generalize the convex duality symmetry in Gibbs' statistical ensemble formulation, between Massieu's free entropy $Φ_{V,N} (β)$ and the Gibbs entropy $φ_{V,N}(u)$ as a function of mean internal energy $u$. The duality tells us that Gibbs thermodynamic entropy is to the law of large numbers (LLN) for arithmetic sample means what Shannon's information entropy is to the LLN for empirical counting frequencies. Following the same logic, we identify $u$ as the conjugate variable to counting frequency, a Hamilton-Jacobi equation for Shannon entropy as an equation of state, and suggest an eigenvalue problem for modeling statistical frequencies of correlated data.

cond-mat.stat-mech↗

arXiv2021

Nonequilibrium Stationary Process and Fluctuation-Dissipation Relations

A stochastic dynamics has a natural decomposition into a drift capturing mean rate of change and a martingale increment capturing randomness. They are two statistically uncorrelated, but not necessarily independent mechanisms contributing to the overall fluctuations of the dynamics, representing the uncertainties in the past and in the future. A generalized Einstein relation is a consequence solely because the dynamics being stationary; and the Green-Kubo formula reflects a balance between the two mechanisms. Equilibrium with reversibility is characterized by a novel covariance symmetry.

cond-mat.stat-mech↗

arXiv2021

Potentials of Continuous Markov Process and Random Perturbations

With a scalar potential and a bivector potential, the vector field associated with the drift of a diffusion is decomposed into a generalized gradient field, a field perpendicular to the gradient, and a divergence-free field. We give such decomposition a probabilistic interpretation by introducing cycle velocity from a bivectorial formalism of nonequilibrium thermodynamics. New understandings on the mean rates of thermodynamic quantities are presented. Deterministic dynamical system is further proven to admit a generalized gradient form with the emerged potential as the Lyapunov function by the method of random perturbations.

cond-mat.stat-mech↗

arXiv2020

Bivectorial Nonequilibrium Thermodynamics: Cycle Affinity, Vorticity Potential, and Onsager's Principle

We generalize an idea in the works of Landauer and Bennett on computations, and Hill's in chemical kinetics, to emphasize the importance of kinetic cycles in mesoscopic nonequilibrium thermodynamics (NET). For continuous stochastic systems, a NET in phase space is formulated in terms of cycle affinity $\nabla\wedge\big(\mathbf{D}^{-1}\mathbf{b}\big)$ and vorticity potential $\mathbf{A}(\mathbf{x})$ of the stationary flux $\mathbf{J}^{*}=\nabla\times\mathbf{A}$. Each bivectorial cycle couples two transport processes represented by vectors and gives rise to Onsager's reciprocality; the scalar product of the two bivectors $\mathbf{A}\cdot\nabla\wedge\big(\mathbf{D}^{-1}\mathbf{b}\big)$ is the rate of local entropy production in the nonequilibrium steady state. An Onsager operator that maps vorticity to cycle affinity is introduced.

cond-mat.stat-mech↗

arXiv2020

Kinematic Basis of Emergent Energetics of Complex Dynamics

Stochastic kinematic description of a complex dynamics is shown to dictate an energetic and thermodynamic structure. An energy function $φ(x)$ emerges as the limit of the generalized, nonequilibrium free energy of a Markovian dynamics with vanishing fluctuations. In terms of the $\nablaφ$ and its orthogonal field $γ(x)\perp\nablaφ$, a general vector field $b(x)$ can be decomposed into $-D(x)\nablaφ+γ$, where $\nabla\cdot\big(ω(x)γ(x)\big)=$ $-\nablaωD(x)\nablaφ$. The matrix $D(x)$ and scalar $ω(x)$, two additional characteristics to the $b(x)$ alone, represent the local geometry and density of states intrinsic to the statistical motion in the state space at $x$. $φ(x)$ and $ω(x)$ are interpreted as the emergent energy and degeneracy of the motion, with an energy balance equation $dφ(x(t))/dt=γD^{-1}γ-bD^{-1}b$, reflecting the geometrical $\|D\nablaφ\|^2+\|γ\|^2=\|b\|^2$. The partition function employed in statistical mechanics and J. W. Gibbs' method of ensemble change naturally arise; a fluctuation-dissipation theorem is established via the two leading-order asymptotics of entropy production as $ε\to 0$. The present theory provides a mathematical basis for P. W. Anderson's emergent behavior in the hierarchical structure of complexity science.

physics.gen-ph↗

arXiv2020

Unified formalism for entropy productions and fluctuation relations

Stochastic entropy production, which quantifies the difference between the probabilities of trajectories of a stochastic dynamics and its time reversals, has a central role in nonequilibrium thermodynamics. In the theory of probability, the change in the statistical properties of observables can be represented by a change in the probability measure. We consider operators on the space of probability measure that induce changes in the statistical properties of a process, and formulate entropy productions in terms of these change-of-probability-measure (CPM) operators. This mathematical underpinning of the origin of entropy productions allows us to achieve an organization of various forms of fluctuation relations: All entropy productions have a non-negative mean value, admit the integral fluctuation theorem, and satisfy a rather general fluctuation relation. Other results such as the transient fluctuation theorem and detailed fluctuation theorems then are derived from the general fluctuation relation with more constraints on the operator. We use a discrete-time, discrete-state-space Markov process to draw the contradistinction among three reversals of a process: time reversal, protocol reversal and the dual process. The properties of their corresponding CPM operators are examined, and the domains of validity of various fluctuation relations for entropy productions in physics and chemistry are revealed. We also show that our CPM operator formalism can help us rather easily extend other fluctuations relations for excess work and heat, discuss the martingale properties of entropy productions, and derive the stochastic integral formulas for entropy productions in constant-noise diffusion process with Girsanov theorem. Our formalism provides a general and concise way to study the properties of entropy-related quantities in stochastic thermodynamics and information theory.

cond-mat.stat-mech↗

arXiv2015

Adaptive Synchronization and Anticipatory Dynamical System

Many biological systems can sense periodical variations in a stimulus input and produce well-timed, anticipatory responses after the input is removed. Such systems show memory effects for retaining timing information in the stimulus and cannot be understood from traditional synchronization consideration of passive oscillatory systems. To understand this anticipatory phenomena, we consider oscillators built from excitable systems with the addition of an adaptive dynamics. With such systems, well-timed post-stimulus responses similar to those from experiments can be obtained. Furthermore, a well-known model of working memory is shown to possess similar anticipatory dynamics when the adaptive mechanism is identified with synaptic facilitation. The last finding suggests that this type of oscillators can be common in neuronal systems with plasticity.

q-bio.NC↗