统计力学
Stochastic gradient descent (SGD) is a fundamental tool for training deep neural networks across a variety of tasks. In self-supervised learning, different input categories map to distinct manifolds in the embedded neural state space.…
We study a simple one dimensional sluggish random walk model with subdiffusive growth. In the continuum hydrodynamic limit, the model corresponds to a particle diffusing on a line with a space dependent diffusion constant D(x)=…
Will the strategy of resetting} help a stochastic process to reach its target efficiently, with its environment continually toggling between a strongly favourable and an unfavourable (or weakly favourable) state? A diffusive run-and-tumble…
The changeover from first-order to second-order phase transitions in q-state Potts models is obtained at q_c=2 in spatial dimension d=3 and essentially at q_c=4 in d=2, using a physically intuited simple adaptation of the Migdal-Kadanoff…
Dispersal is often used by living beings to gather information from conspecifics, integrating it with personal experience to guide decision-making. This mechanism has only recently been studied experimentally, facilitated by advancements in…
In 1988, Constantino Tsallis proposed an extension of the Boltzmann statistical mechanics by postulating a new entropy formula, $S_q = k_B\ln_q W$, where $W$ is the number of microstates accessible to the system, and $\ln_q$ defines a…
Mechanochemical patterns arising in the actomyosin cortex drive many cellular processes. Here we consider a hydrodynamic model for the actomyosin cortex of cells and study the sensitivity of the emergent patterns to both physical parameters…
We propose a simple model of quantum void where the flow of time is deduced directly from quantum fluctuations and the consequent particle-antiparticle creations. Given a certain number of space-like separated pair creation events, assumed…
It is known that on directed graphs, the correlations between neighbours of a given site vanish and thus simple mean-field-like arguments can be used to describe exactly the behaviour of Ising-like systems. We analyse heterogeneous…
The contact value theorem was originally derived for Coulomb fluids of mobile charged particles in thermal equilibrium, in the presence of interfaces carrying a {\em uniform} surface charge density and in the absence of dielectric…
The emergence of diffusion is one of the deepest physical phenomena observed in many-body interacting, chaotic systems. But establishing rigorously that correlation functions, say of the spin, expand diffusively, remains one of the most…
The fractional Ornstein-Uhleneck (fOU) process is described by the overdamped Langevin equation $\dot{x}(t)+\gamma x=\sqrt{2 D}\xi(t)$, where $\xi(t)$ is the fractional Gaussian noise with the Hurst exponent $0<H<1$. For $H\neq 1/2$ the fOU…
Long-range correlations manifested as power spectral density scaling $1/f^\beta$ for frequency $f$ and a range of exponents $\beta$ are investigated for a superposition of uncorrelated pulses with distributed durations $\tau$. Closed-form…
At long times, a fractional Brownian particle in a confining external potential reaches a non-equilibrium (non-Boltzmann) steady state. Here we consider scale-invariant power-law potentials $V(x)\sim |x|^m$, where $m>0$, and employ the…
We explore the critical properties of the recently discovered finite-time dynamical phase transition in the non-equilibrium relaxation of Ising magnets after a temperature quench. The transition is characterized by a sudden switch in the…
We introduce and study analytically and numerically a simple model of inter-agent competition, where underachievement is strongly discouraged. We consider $N\gg 1$ particles performing independent Brownian motions on the line. Two particles…
The propagation of the effects connected with the occurrence of magnetization reversals in an amorphous ribbon of Fe$_{63}$B$_{64}$Si$_{8}$Ni$_{15}$ has been investigated using a method based on two pickup coils separated by a distance…
Non-Gaussian noise is omnipresent in systems where the central-limit theorem is inapplicable. We here investigate the stochastic thermodynamics of small systems that are described by a general Kramers-Moyal equation that includes both…
We consider a microscopic model of an inhomogeneous environment where an arbitrary quantum system is locally coupled to a harmonic bath via a finite-range interaction. We show that in the overdamped regime the position distribution obeys a…
Individual components such as cells, particles, or agents within a larger system often require detailed understanding of their relative position to act accordingly, enabling the system as a whole to function in an organised and efficient…