Statistical Mechanics
We investigate the search of a target with a given spatial distribution in a finite one-dimensional domain. The searcher follows Brownian dynamics and is always reset to its initial position when reaching the boundaries of the domain…
Time-delayed effects are widely present in nature, often accompanied by distinctive nonequilibrium features, such as negative apparent heat dissipation. To elucidate detailed structures of the dissipation, we study the frequency…
We investigate site and bond percolation in triangular and square lattices subjected to linear distortion. In contrast to previously studied distortion schemes that preserve lattice geometry, linear distortion dislocates regular lattice…
Run-and-tumble particles constitute one of the simplest models of self-propelled active matter, and provide an ideal playground to the understanding of out-of-equilibrium systems. We consider an idealized setup where one such particle is…
We present an exact method for calculating the large deviation function describing rare fluctuations in the number of particles for product-kernel aggregation. Starting from the master equation, we derive an exact integral representation…
We study the statistical properties of the area and the absolute area under the trajectories of subdiffusive random walks. Using different frameworks to describe subdiffusion (as the scaled Brownian motion, fractional Brownian motion, the…
We provide a rigorous first-principle derivation of the non-additive Tsallis' entropy by employing the Chaitin-Kolmogorov algorithmic information theory. By applying non-local restrictive rules on the string formation (grammar), we show…
We study site percolation on a square lattice with random compact diamond-shaped neighborhoods. Each site $s$ is connected to others within a neighborhood in the shape of a diamond of radius $r_s$, where $r_s$ is uniformly chosen from the…
At the nanoscale, random effects govern not only the dynamics of a physical system but may also affect its observation. This work introduces a novel paradigm for coarse graining that eschews the assignment of a unique coarse-grained…
We present a bipartite network model that captures intermediate stages of optimization by blending the Maximum Entropy approach with Optimal Transport. In this framework, the network's constraints define the total mass each node can supply…
In the context of first-passage percolation (FPP), we investigate the statistical properties of the selected link-times (SLTs) -the random link times comprising the optimal paths (or geodesics) connecting two given points. We focus on…
We study quantum spin chains solvable via hidden free fermionic structures. We study the algebras behind such models, establishing connections to the mathematical literature of the so-called ``graph-Clifford'' or ``quasi-Clifford''…
We investigate non-equilibrium phase coexistence associated with a first-order phase transition by numerically studying a one-dimensional Hamiltonian-Potts model with fractional spatial derivatives. The fractional derivative is introduced…
We study the emergence of statistical mechanics in isolated classical systems with local interactions and discrete phase spaces. We establish that thermalization in such systems does not require global ergodicity; instead, it arises from…
We investigate the statistical correlation between the first-reaction time of a diffusing particle and its boundary local time accumulated until the reaction event. Since the reaction event occurs after multiple encounters of the particle…
Inspired by recent studies on deterministic oscillator models, we introduce a stochastic one-dimensional model for a chain of interacting particles. The model consists of $N$ oscillators performing continuous-time random walks on the…
We provide an exact analytical solution of the single-particle Schr\"odinger equation for a chain of non-interacting fermions subject to a time-dependent linear potential, with its slope varied as an arbitrary function of time. The…
We consider the Blume--Capel model in the scaling limit to realize the thermal perturbation of the tricritical Ising fixed point. We develop a numerical scaling limit extrapolation for one-point functions and R\'enyi entropies in the ground…
We propose an extended structural dynamics framework that enriches classical mechanics by treating particle orientation and internal structure as fundamental phase-space coordinates. This extension preserves Hamiltonian structure and…
Criticality has been proposed as a mechanism for the emergence of complexity, life, and computation, as it exhibits a balance between robustness and adaptability. In classic models of complex systems where structure and dynamics are…