Statistical Mechanics
We study connections between discrete probability distributions and the statistical mechanics of small systems. Using probability generating functions, we develop the theory of power series, infinitely divisible, and scalable distributions…
Kinesin is a molecular motor that transports intracellular cargoes along microtubules. Recent studies have quantified kinesin performance using various efficiencies within the framework of stochastic thermodynamics; however, quantitative…
We investigate deterministic coarsening dynamics in a spatially extended bistable gene toggle model with diffusive coupling. Unlike classical curvature-driven coarsening, where domain walls move continuously and annihilate gradually, the…
Systems of hard rods of equal length in a one-dimensional harmonic trap have been observed to exhibit peculiar non-ergodic behavior that might suggest the existence of a novel hidden conserved quantity beyond the two well known ones, i.e.,…
Highly excited quantum states at the critical boundary of ergodicity are known to deviate from thermal behavior, yet their dynamical properties remain poorly understood. Here, we uncover the complexity of quantum dynamics at criticality…
We consider a system of non-interacting fermions prepared in the many-body ground state of an isotropic trapping potential in any dimension, and investigate the ballistic expansion of the fermionic cloud after the potential is suddenly…
The present paper is a study of the large scale properties of the Kuramoto-Sivashinsky equation. By using a Schwinger-Dyson framework, we aim to provide a proof that the only solutions that can sustain a stable scaling in the infrared limit…
The maximization of statistical complexity has long been associated with the emergence of probability distributions lying between perfect order and complete disorder. While previous studies have shown that complexity-maximizing…
We show that the Belopol'skaya-Daletskii formulation of stochastic differential equations on a Riemann manifold offers an elementary way to construct equivariant representations of finite-dimensional approximations to the path measure of a…
Richards' equation for unsaturated water flow is derived from the kinetic theory of the pore-filling distribution g(r,x,t) of a companion paper. It separates two limits that macroscopic theory usually conflates. The spatial limit is purely…
The adverse-selection mechanism in markets explains how asymmetric information between buyers and sellers can drive high-quality goods out of the market, thereby causing market deterioration. In its simplest formulation, only the mean…
Technologies for artificially controlling chemical reaction systems, such as optogenetics, are rapidly advancing, making it increasingly important to understand reaction dynamics under time-dependent control. When the modulation of reaction…
A vertex-reinforced random walk steps to a neighbour with probability proportional to $1+\beta n^{a}$, where $n$ counts previous visits to that neighbour and $a\in(0,1)$ sets the memory strength. On the rooted $b$-ary tree the exponential…
Biological systems across scales, along with many engineering problems, must control noisy systems with limited information. Here we study information-limited feedback control of stochastic systems to achieve target steady states, and…
We solve the two models for Glauber dynamics and in equilibrium, both in the presence and absence of the external magnetic field on a complete graph. We compare the steady state of the Glauber dynamics with equilibrium and find that for low…
Machine-learning detection of phase transitions depends not only on the learning algorithm, but also on whether the input representation preserves the symmetries of the system. We examine this for the weak first-order isotropic--nematic…
Maxwell demons can convert knowledge into thermodynamic advantage by using measurement-acquired information. However, standard formulations of this problem assume that the demon has access to the system's entire phase space, an assumption…
We investigate the nonequilibrium ordering dynamics of coupled Kuramoto oscillators with negative nearest-neighbor coupling, which induces a zigzag antiferromagnetic ordering. In one dimension, the defect density exhibits anomalously slow…
We investigate the ultrametric organization of energy landscapes defined on sparse random Erd\H{o}s--R\'enyi graphs. Each graph vertex is assigned a random free energy from a uniform distribution over an interval of width $\Delta F$, and…
We revisit the renormalization group (RG) approach to the one-dimensional stochastic Kuramoto-Sivashinsky (KS) equation and show that previous approaches based on perturbative Wilsonian RG with a sharp cutoff are not valid, even though they…