统计力学
I revisit the Galam Majority Model (GMM) with contrarian agents from a statistical-mechanics perspective, revealing three fundamental features. First, in addition to the GMM simultaneous-update of small discussion groups, I construct a…
We derive a general relation between the velocity and force autocorrelation tensors (VACT and FACT) for a Brownian particle subject to an external magnetic field. Using time-symmetry arguments, we show that, for the full Langevin dynamics,…
If a generalized Langevin equation contains a potential of mean force, it cannot at the same time contain a linear memory kernel and a fluctuating force that obeys a second fluctuation dissipation theorem in the sense of Kubo, and be exact.…
Remarkably common statistical laws characterize the diversity scaling and its fluctuations across a wide range of complex "component systems". These regularities are often interpreted as signatures of an underlying innovation mechanism…
It has been known for several decades that the third moment of the multifractal spectrum of the harmonic measure for diffusion-limited aggregates is linked to the underlying fractal dimension of the cluster. We demonstrate, using an…
We investigate homogeneous populations of smart active agents that exchange information with their neighbors to perform a decentralized learning process aimed at achieving a prescribed macroscopic state. Such agents may, for example,…
Attention enables a world model to condition on its entire history, providing long-term memory that facilitates long-range predictions. While the local Onsager--Machlup theory in our companion paper assumes a temporally local predictive…
We investigate the sandpile model on complex networks by developing a branching-process framework that explicitly incorporates dissipation during avalanche propagation. Unlike classical branching descriptions, which assume conservative…
We derive the distribution of the first passage time $t_{fp}$ for the position $x$ of an underdamped harmonic oscillator to overcome a threshold $x_B$. As the $t_{fp}$ distribution depends on the oscillator quality factor $Q$ different…
The distribution of the first passage time $t_{fp}$ for the position $x$ to overcome a threshold $x_B$ is calculated in an underdamped harmonic oscillator. The proof combines several approaches based on the determination of the eigenvalues…
This review discusses the recently proposed fuzzy sphere regularization for studying $2+1$D critical phenomena, particularly three-dimensional (3D) conformal field theory (CFT). The fuzzy sphere scheme not only offers remarkable efficiency…
Active systems can exhibit a broad range of phenomena forbidden in equilibrium. Their dynamics are often specified by abstract local update rules, and it is generally unclear when the same behavior can arise from physically natural driving.…
While imaginary-time evolution has long served as a standard paradigm for ground-state preparation in numerical simulations and quantum devices, its intrinsic dynamical properties has been largely overlooked. Here, we investigate the…
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…