Statistical Mechanics
A double-occupancy cell model of a fluid with Curie-Weiss interaction is studied. First, we show that the model is isomorphic to the Blume-Capel model on a complete graph through a simple transformation from spin to occupancy variables. We…
Ruggedness of the underlying energy landscape gives rise to heterogeneous mobility and non-Gaussian diffusion. We develop a theoretical framework for tagged-particle diffusion in multidimensional rugged energy landscapes modeled as…
Complex interactions among regulatory molecules determine the rules underlying cell growth and division in microbial cells. While the governing molecular network may not always be obvious, it is well known that correlations among certain…
We study a slow heat-driven flow in a gas of elastically colliding hard disks confined to a long channel. The initial state consists of two regions with large temperature and density contrasts but nearly equal pressures, leading to a…
We construct directly on the lattice a class of non-unitary interfaces that are both exactly conformal and exactly solvable, and establish their corresponding boundary and interface conformal field theory (CFT) descriptions. The…
The three-dimensional organization of the genome exhibits rich, scale-dependent structure, as revealed by both chromosome contact maps (e.g., Hi-C maps) and chromatin density measured by microscopy. Recent studies have reported multifractal…
Small-scale systems are inherently subject to environmental noise that can be harnessed constructively to realize reliable logic operations -- a phenomenon known as logical stochastic resonance (LSR), where a bistable system produces…
For particles of fixed mass, classical equilibrium statistical mechanics dictates a Maxwellian velocity distribution determined solely by the temperature, regardless of the interactions, density, or structure. Supercooled glass forming…
We study $N$ non-interacting Brownian particles in an external potential under simultaneous stochastic resetting to the origin. Although they do not interact directly, common resets generate strong dynamically emergent correlations (DEC).…
Motivated by the quest for active quantum matter, we investigate the dynamics of an impurity immersed in a quantum gas -- a polaron -- whose coupling to the surrounding medium is periodically modulated in time, alternating in sign. By…
There is strong qualitative empirical evidence in the scientific literature that, due to cognitive fatigue, workers performing repetitive and monotonous tasks are characterized by a gradual deterioration in their performance abilities as…
Integrable quantum systems evolving from non-equilibrium initial states do not thermalize to conventional Gibbs ensembles (GE). Instead, at long times they relax to generalized Gibbs ensembles (GGEs), which incorporate the full set of local…
We show that the effective dynamics of the elitist $(1+M)$ genetic algorithm is, in the limit of small mutations, clipped gradient descent on the loss in the presence of anisotropic Gaussian white noise. In expectation, therefore, a simple…
We develop a field-theoretic framework for work statistics in $O(N)$ models driven through criticality. By analyzing the dynamic renormalization group flow of composite power operators, we find the Kibble-Zurek scaling laws as a natural…
For a process in which a system is driven irreversibly from equilibrium state $A$ toward equilibrium state $B$, the free energy difference $\Delta F = F_B-F_A$ can be estimated using the work fluctuation theorem $\langle e^{-W/T}\rangle =…
The problem of storing secure information on a network is studied. A formal framework for distributed secret storage is introduced, and possible applications in technological and social systems are discussed. The problem is formulated as…
We consider a population dynamics model in which each diffusing particle that hits a catalytic surface can split into two independent copies (clones). The particles of such a growing-in-size population search in parallel for a hidden…
We study stochastic models of a microscopic active heat engine, comprised of an overdamped Brownian particle trapped in a harmonic potential, and in simultaneous contact with thermal (passive) and athermal (active) baths. The interaction…
Continuous space-filling maps can be surjective onto higher-dimensional regions, but thermodynamic protocols are rectifiable finite-resolution paths. We study exhaustive traversal of a compact $d$-dimensional thermodynamic state-space…
Entanglement entropy has proven to be a powerful probe of phenomena such as quantum chaos and phase transitions. Pseudo entropy is a recently proposed time-like generalization of an entanglement measure, motivated by de Sitter holography.…