Related papers: Singular Fluctuation as Specific Heat in Bayesian …
We study the specific heat of a model supercooled liquid confined in a spherical cavity with amorphous boundary conditions. We find the equilibrium specific heat has a cavity-size-dependent peak as a function of temperature. The cavity…
In this article we analyze several mathematical models with singularities where the classical cotangent model is replaced by a $b$-cotangent model. We provide physical interpretations of the singular symplectic geometry underlying in…
We try to design a simple model exhibiting self-organized criticality, which is amenable to a rigorous mathematical analysis. To this end, we modify the generalized Ising Curie-Weiss model by implementing an automatic control of the inverse…
Complex arithmetic random waves are stationary Gaussian complex-valued solutions of the Helmholtz equation on the two-dimensional flat torus. We use Wiener-It\^o chaotic expansions in order to derive a complete characterization of the…
Thermal fluctuations are a fundamental feature of dissipative systems that are essential for understanding physics near the expected critical point of QCD and in small systems. When such fluctuations are modeled naively in relativistic…
Employing numerical simulations, we provide an accurate insight into the of heat transfer mechanisms in the Rayleigh-B\'enard convection of concentrated emulsions with finite-size droplets. We focus on the unsteady dynamics characterizing…
Molecular origin of the well-known specific heat anomaly in supercooled liquid water is investigated here by using extensive computer simulations and theoretical analyses. A rather sharp increase in the values of isobaric specific heat with…
In the framework of BCS model, we have applied the isothermal probability distribution to take into account the statistical fluctuations in calculation of thermodynamical properties of nuclei. The energy and the heat capacity are calculated…
We study the fluctuations of the Gaussian model, with conservation of the order parameter, evolving in contact with a thermal bath quenched from inverse temperature $\beta _i$ to a final one $\beta _f$. At every time there exists a critical…
The behavior of a class of solutions of the shallow water Airy system originating from initial data with discontinuous derivatives is considered. Initial data are obtained by splicing together self-similar parabolae with a constant…
Advances in statistical learning theory have resulted in a multitude of different designs of learning machines. But which ones are implemented by brains and other biological information processors? We analyze how various abstract Bayesian…
We study the effects of thermal fluctuations on symmetric tensionless heterogeneous (two-component) fluid membranes in a simple minimal model. Close to the critical point $T_c$ of the associated miscibility phase transition of the…
There has been an increasing interest in the quantification of nearly deterministic work extraction from a finite number of copies of microscopic particles in finite time. This paradigm, so called single-shot epsilon-deterministic work…
We investigate the singular behavior of information flow near the Hopf bifurcation point by analyzing the learning rate, a key quantity in stochastic thermodynamics. As a model system exhibiting the Hopf bifurcation, we study the…
We consider the single eigenvalue fluctuations of random matrices of general Wigner-type, under a one-cut assumption on the density of states. For eigenvalues in the bulk, we prove that the asymptotic fluctuations of a single eigenvalue…
Liquids near the glass transition exhibit dynamical heterogeneity, i.e. correlated regions in the liquid relax at either a much faster rate or a much slower rate than the average. This collective phenomenon has been characterized by…
Time-integrated quantities such as work and heat increase incessantly in time during nonequilibrium processes near steady states. In the long-time limit, the average values of work and heat become asymptotically equivalent to each other,…
Temperature fluctuations in an atmospheric convective boundary layer are investigated by means of Large Eddy Simulations (LES). A statistical characterization for both weak temperature fluctuations and strong temperature fluctuations has…
We expand upon a natural analogy between Bayesian statistics and statistical physics in which sample size corresponds to inverse temperature. This analogy motivates the definition of two novel statistical quantities: a learning capacity and…
The characteristic function for heat fluctuations in a non equilibrium system is characterised by a large deviation function whose symmetry gives rise to a fluctuation theorem. In equilibrium the large deviation function vanishes and the…