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The variable two-step backward differentiation formula (BDF2) is revisited via a new theoretical framework using the positive semi-definiteness of BDF2 convolution kernels and a class of orthogonal convolution kernels. We prove that, if the…
The concept of entropy has been pivotal in the formulation of thermodynamics. For systems driven away from thermal equilibrium, a comparable role is played by entropy production and dissipation. Here we provide a comprehensive picture how…
In this paper, a class of reaction-diffusion equations for Multiple Sclerosis is presented. These models are derived by means of a diffusive limit starting from a proper kinetic description, taking account of the underlying microscopic…
The classical evolution equations of the Abelian Higgs model are studied at temperatures below the Ginsburg temperature of a phase transition which is assumed to be second order. It is shown that the initial thermal fluctuations provide a…
The incredible thermo-mechanical properties of biological materials arise from the microscopic scale due to a complex hierarchical mechanism, regulated by microinstabilities at the molecular level. The description of such complex structures…
We study diffusion-controlled processes in nonequilibrium steady states, where standard rate theory assumptions break down. Using transition path theory, we generalize the relations between reactive probability fluxes and measures of the…
We present a general method to undertake a thorough analysis of the thermodynamics of the quantum jump trajectories followed by an arbitrary quantum harmonic network undergoing linear and bilinear dynamics. The approach is based on the…
The stationary points of the potential energy function V are studied for the \phi^4 model on a two-dimensional square lattice with nearest-neighbor interactions. On the basis of analytical and numerical results, we explore the relation of…
Recently, is has been observed that events with the {\it same} total transverse energy of light charged particles (LCP) in the quasi target region, $E_{\perp 12}^{QT}$, show two quite distinct reaction scenarios in the projectile domain:…
In this article we review the thermodynamics of liquids in the framework of the inherent structure formalism. We then present calculations of the distribution of the basins in the potential energy of a binary Lennard-Jones mixture as a…
We address two issues in the thermodynamic model for nuclear disassembly. Surprisingly large differences in results for specific heat were seen in predictions from the canonical and grand canonical ensembles when the nuclear system passes…
Thermodynamics could be seen as an expression of physics at a high epistemic level. As such, its potential as an inductive bias to help machine learning procedures attain accurate and credible predictions has been recently realized in many…
The quest for ever higher information capacities has brought about a renaissance in multimode optical waveguide systems. This resurgence of interest has recently initiated a flurry of activities in nonlinear multimode fiber optics. The…
We address the problem of the foundation of generalized ensembles in statistical physics. The approach is based on Boltzmann's concept of orthodes. These are the statistical ensembles that satisfy the heat theorem, according to which the…
Akin to the traditional quasi-classical trajectory method for investigating the dynamics on a single adiabatic potential energy surface for an elementary chemical reaction, we carry out the dynamics on a 2-state ab initio potential energy…
A thermodynamic phase transition denotes a drastic change of state of a physical system due to a continuous change of thermodynamic variables, as for instance pressure and temperature. The classical van der Waals equation of state is the…
Recently implemented quantum devices such as quantum processors and quantum simulators combine highly complicated quantum dynamics with high-resolution measurements. We present a passivity deformation methodology that sets thermodynamic…
A major part of the many thermally driven processes in our natural environment as well as in engineering solutions of Carnot-type machinery is based on the second law of thermodynamics (or principle of entropy increase). An interesting link…
Dissipative particle dynamics (DPD) does not conserve energy and this precludes its use in the study of thermal processes in complex fluids. We present here a generalization of DPD that incorporates an internal energy and a temperature…
This paper presents an overview of recent computer simulations of grain boundary (GB) diffusion focusing on atomistic understanding of diffusion mechanisms. At low temperatures when GB structure is ordered, diffusion is mediated by point…