Berg, Marcus
Published in
Journal of Statistical Mechanics: Theory and Experiment

Using recent results in mathematics, I point out that free energies and scale-dependent central charges away from criticality can be represented in compact form where modular invariance is manifest. The main example is the near-critical Ising model on a thermal torus, but the methods are not restricted to modular symmetry, and apply to automorphic ...

Nurcombe, Madeline
Published in
Journal of Statistical Mechanics: Theory and Experiment

We introduce the ghost algebra, a two-boundary generalisation of the Temperley–Lieb (TL) algebra, using a diagrammatic presentation. The existing two-boundary TL algebra has a basis of string diagrams with two boundaries, and the number of strings connected to each boundary must be even; in the ghost algebra, this number may be odd. To preserve ass...

Xie, Rongrong Marsili, Matteo
Published in
Journal of Statistical Mechanics: Theory and Experiment

We discuss the concept of probabilistic neural networks with a fixed internal representation being models for machine understanding. Here, ‘understanding’ is interpretted as the ability to map data to an already existing representation which encodes an a priori organisation of the feature space. We derive the internal representation by requiring th...

Guo, Wusong Yan, Hao Chen, Hanshuang
Published in
Journal of Statistical Mechanics: Theory and Experiment

We study the extreme value statistics of first-passage trajectories generated from a one-dimensional drifted Brownian motion subject to stochastic resetting to the starting point with a constant rate r. Each stochastic trajectory starts from a positive position x 0 and terminates whenever the particle hits the origin for the first time. We obtain a...

Plyukhin, Alex V
Published in
Journal of Statistical Mechanics: Theory and Experiment

We consider a classical Brownian oscillator of mass m driven from an arbitrary initial state by varying the stiffness k(t) of the harmonic potential according to the protocol k(t)=k0+aδ(t) , involving the Dirac delta function. The microscopic work performed on the oscillator is shown to be W=(a2/2m)q2−aqv , where q and v are the coordinate and velo...

Mukherjee, Sukanta Pareek, Puneet Barma, Mustansir Kumar Nandi, Saroj
Published in
Journal of Statistical Mechanics: Theory and Experiment

The autocorrelation function in many complex systems shows a crossover in the form of its decay: from a stretched exponential relaxation (SER) at short times to a power law at long times. Studies of the mechanisms leading to such multiple relaxation patterns are rare. Additionally, the inherent complexity of these systems makes it hard to understan...

Mabillard, Joël Gaspard, Pierre
Published in
Journal of Statistical Mechanics: Theory and Experiment

Within the framework of the local equilibrium approach, the equilibrium and nonequilibrium properties relevant to the hydrodynamics of the perfect hard-sphere crystal were obtained through molecular dynamics simulations using the Helfand moments associated with momentum and energy transport. Because this crystal is face-centered cubic, the hydrodyn...

Lee, Chern Ye, Hai Li, Hui
Published in
Journal of Statistical Mechanics: Theory and Experiment

Stochastic differential equations (SDEs) play an important role in fields ranging from physics and biology to economics. The interpretation of stochastic calculus in the presence of multiplicative noise continues to be an open question. Commonly, the choice of stochastic calculus rules is largely based on empirical knowledge and lacks quantitative ...

Kaneko, Kunihiko
Published in
Journal of Statistical Mechanics: Theory and Experiment

The possibility of establishing a macroscopic phenomenological theory for biological systems, akin to the well-established framework of thermodynamics, is briefly reviewed. We introduce the concept of an evolutionary fluctuation–response relationship, which highlights the tight correlation between the variance in phenotypic traits caused by genetic...

Moueddene, Leïla G Fytas, Nikolaos Holovatch, Yurij Kenna, Ralph Berche, Bertrand
Published in
Journal of Statistical Mechanics: Theory and Experiment

We show that accurate insights into the critical properties of the Blume–Capel model at two dimensions can be deduced from Monte Carlo simulations, even for small system sizes, when one analyses the behaviour of the zeros of the partition function. The phase diagram of the model displays a line of second-order phase transitions ending at a tricriti...