Related papers: Tropical Limit for Configurational Geometry in Dis…
It is possible to formulate the thermodynamics of a glass forming system in terms of the properties of inherent structures, which correspond to the minima of the potential energy and build up the potential energy landscape in the…
In the field of classical discrete systems, specifically substitutional alloys, this study introduces a stochastic thermodynamic approach to address nonlinearity within a canonical ensemble. This approach establishes a nonlinear…
We consider in this review the statistical mechanical description of a very general microscopic lattice model of a compressible and interacting multi-component mixture of linear polymers of fixed lengths. The model contains several…
We compute the temperature-dependent barrier for alpha-relaxations in several liquids, without adjustable parameters, using experimentally determined elastic, structural, and calorimetric data. We employ the random first order…
Potential energy landscape (PEL) is essential to determine phase stability, reaction path, and other important physical as well as chemical properties. Whereas given PEL can reasonably determine the properties in thermodynamically…
Tropical limit for macroscopic systems in equilibrium defined as the formal limit of Boltzmann constant k going to 0 is discussed. It is shown that such tropical limit is well-adapted to analyse properties of systems with highly degenerated…
The thermodynamics for a system with given temperature, density, and volume is described by the Canonical ensemble. The thermodynamics for a corresponding system with the same temperature, volume, and average density is described by the…
Time-dependent density-functional theory (TDDFT) is a central tool for studying the dynamical electronic structure of molecules and solids, yet aspects of its mathematical foundations remain insufficiently understood. In this work, we…
There is an ever-growing need for predictive models for the elasto-viscoplastic deformation of solids. Our goal in this paper is to incorporate recently developed out-of-equilibrium statistical concepts into a thermodynamically consistent,…
A statistical mechanical distance constraint model (DCM) is presented that explicitly accounts for network rigidity among constraints present within a system. Constraints are characterized by local microscopic free energy functions.…
We study a class of models for brittle fracture: elastic theory models which allow for cracks but not for plastic flow. We show that these models exhibit, at all finite temperatures, a transition to fracture under applied load similar to…
We propose a variational formulation for the nonequilibrium thermodynamics of discrete open systems, i.e., discrete systems which can exchange mass and heat with the exterior. Our approach is based on a general variational formulation for…
Based on statistical mechanics, a macroscopically homogeneous system, i.e., a single phase in the present context, is composed of many independent configurations that the system embraces. The macroscopical properties of the system are…
We investigate the formation of polycrystalline structures in a class of particle systems. The atomistic energy is modeled as a sum of particle energies that favor atoms being locally isometric to a reference lattice. The discrete frame…
When we consider canonical average for classical discrete systems under constant composition (specifically, substitutional alloys) as a map phi from a set of many-body interatomic interactions to that of microscopic configuration in…
We show that thermodynamics can be formulated naturally from the intrinsic geometry of phase space alone-without postulating an ensemble, which instead emerges from the geometric structure itself. Within this formulation, phase transitions…
Thermal contact is the archetype of non-equilibrium processes driven by constant non-equilibrium constraints enforced by reservoirs exchanging conserved microscopic quantities. In models with a finite number of possible configurations, if…
In this paper, we develop a variational foundation for stochastic thermodynamics of finite-dimensional, continuous-time systems. Requiring the second law (non-negative average total entropy production) systematically yields a consistent…
The usual formulation of thermodynamics is based on the additivity of macroscopic systems. However, there are numerous examples of macroscopic systems that are not additive, due to the long-range character of the interaction among the…
A model of low-temperature polar liquids is constructed that accounts for configurational heat capacity, entropy, and the effect of a strong electric field on the glass transition. The model is based on Pad{\'e}-truncated perturbation…