Statistical Mechanics
We show through theory and numerical experiments that a straightforward calculation of entropy production on short molecular dynamics trajectories allows estimating free-energy barriers and identifying optimal reaction coordinates of…
Functional laws of large numbers (FLLNs) describe the mean-field trajectory of epidemics on networks, but say nothing about the fluctuations around it. These fluctuations are governed by moments of the degree distribution not relevant at…
Battery discharging is governed by a fundamental trade-off between output power and energy conversion efficiency due to internal dissipation. In this paper, we demonstrate that such a trade-off universally yields a parabolic envelope…
We present a complete field-theoretical renormalization-group (RG) analysis of the Brownian Ising Model (BIM), in which a $\mathbb{Z}_2$ order parameter is coupled to a passive conserved density, breaking detailed balance. Using the…
The Ising universality class is remarkably robust to non-equilibrium perturbations, which generically flow to zero under renormalization. We show that this robustness fails when an order parameter is coupled nonreciprocally to a conserved…
We develop a quantitative theory for the emergence of quantum many-body chaos as integrability is broken via a tunable parameter. In a circuit model of free fermions, 'doped' with a tunable density of integrability-breaking gates, we…
We study the nonequilibrium dynamics following a quantum quench in spin chains that can be solved via a mapping to free fermions in disguise. These models feature an exponential degeneracy of all energy eigenvalues, raising the question of…
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…