相关论文: On Aviles-Giga limit states with $L^p$ entropy pro…
Weak solutions $m\colon\Omega\subset\mathbb{R}^2\to\mathbb{R}^2$ of the eikonal equation \begin{align*} |m|=1\text{ a.e. and }\mathrm{div}\: m =0\,, \end{align*} arise naturally as sharp interface limits of bounded energy configurations in…
Given any strictly convex norm $\|\cdot\|$ on $\mathbb{R}^2$ that is $C^1$ in $\mathbb{R}^2\setminus\{0\}$, we study the generalized Aviles-Giga functional \[I_{\epsilon}(m):=\int_{\Omega} \left(\epsilon \left|\nabla m\right|^2 +…
The Eikonal equation arises naturally in the limit of the second order Aviles-Giga functional whose $\Gamma$-convergence is a long standing challenging problem. The theory of entropy solutions of the Eikonal equation plays a central role in…
The Aviles-Giga functional $I_{\epsilon}(u)=\int_{\Omega} \frac{\left|1-\left|\nabla u\right|^2\right|^2}{\epsilon}+\epsilon \left|\nabla^2 u\right|^2 \, dx$ is a well known second order functional that models phenomena from blistering to…
We establish large deviation principles (LDPs) for empirical measures associated with a sequence of Gibbs distributions on $n$-particle configurations, each of which is defined in terms of an inverse temperature $% \beta_n$ and an energy…
The Aviles Giga functional is a well known second order functional that forms a model for blistering and in a certain regime liquid crystals, a related functional models thin magnetized films. Given Lipschitz domain $\Omega\subset R^2$ the…
For vector fields on a two-dimensional domain, we study the asymptotic behaviour of Modica-Mortola (or Allen-Cahn) type functionals under the assumption that the divergence converges to $0$ at a certain rate, which effectively produces a…
A typical strategy of realizing an adiabatic change of a many-particle system is to vary parameters very slowly on a time scale $t_\text{r}$ much larger than intrinsic equilibration time scales. In the ideal case of adiabatic state…
We examine the minimization of information entropy for measures on the phase space of bounded domains, subject to constraints that are averages of grand canonical distributions. We describe the set of all such constraints and show that it…
We consider a generic one dimensional spin system of length $ L $, arbitrarily large, with strictly local interactions, for example nearest neighbor, and prove that the dynamical $ \alpha $-R\'enyi entropies, $ 0 < \alpha \le 1 $, of an…
A run-and-tumble particle in a one dimensional box (infinite potential well) is studied. The steady state is analytically solved and analyzed, revealing the emergent length scale of the boundary layer where particles accumulate near the…
Entropy production is often interpreted as a proxy for microscopic disorder or environmental roughness in stochastic systems. We test this interpretation using controlled simulations of overdamped stochastic dynamics on curved surfaces in…
Convex integration has revealed that the Euler system of gas dynamics is ill-posed in the class of weak solutions even if the entropy inequality is imposed as an additional constraint. A natural question arises, namely, if a physically…
Entropy production is the crucial quantity characterizing irreversible phenomena and the second law of thermodynamics. Yet, a ubiquitous definition eludes consensus. Given that entropy production arises from incomplete access to…
The exact expression for the entropy current of a fluid in presence of two dimensional gravitational anomalies is given. To make it compatible with the second law of thermodynamics; i.e. positivity of the entropy production rate of a system…
We investigate entropy production in the small-mass (or overdamped) limit of Langevin-Kramers dynamics. The results generalize previous works to provide a rigorous derivation that covers systems with magnetic field as well as anisotropic…
Entropy production in multiparticle systems is investigated by analysing the experimental data on ion-ion collision at AGS and SPS energies and comparing the findings with those reported earlier for hadron-hadron, hadron-nucleus and…
Motivated by some models of pattern formation involving an unoriented director field in the plane, we study a family of unoriented counterparts to the Aviles-Giga functional. We introduce a nonlinear curl operator for such unoriented vector…
This is a short review of the statistical mechanical definition of entropy production for systems composed of a large number of interacting components. Emphasis is on open systems driven away from equilibrium where the entropy production…
The minimum rate of entropy production (MREP) and the least dissipation energy (LDE) principles are re-examined concerning continuous systems in stationary nonequilibrium states. By means of simple considerations on coefficients of…