Related papers: Microscopic Geometry Characterizes Structure/Poten…
In the present work, we discuss how the functional form of thermodynamic observables can be deduced from the geometric properties of subsets of phase space. The geometric quantities taken into account are mainly extrinsic curvatures of the…
Partial differential equations can be solved on general polygonal and polyhedral meshes, through Polytopal Element Methods (PEMs). Unfortunately, the relation between geometry and analysis is still unknown and subject to ongoing research in…
Binary mixtures are known to phase separate via both nucleation and spinodal decomposition, depending on the initial composition and extent of the quench. Here we develop an energy landscape view of phase separation and non-ideality in…
We explore how the thermodynamic properties and dynamics of a self-interstitial prismatic dislocation loop are affected by microscopic-scale variations in its geometric configuration, an aspect that rarely received attention in literature.…
Particles interacting with short-ranged potentials have attracted increasing interest, partly for their ability to model mesoscale systems such as colloids interacting via DNA or depletion. We consider the free energy landscape of such…
The modern thermodynamics of discrete systems is based on graph theory, which provides both algebraic methods to define observables and a geometric intuition of their meaning and role. However, because chemical reactions are usually…
Supercooled liquids are metastable states realized by suppressing crystallization below the melting temperature. While it is well established that their dynamics slow down dramatically and become spatially heterogeneous upon cooling, the…
For classical discrete systems with constant composition (typically referred to substitutional alloys) under thermodynamically equilibrium state, macroscopic structure should in principle depend on temperature and many-body interaction…
For studying the thermodynamic properties of systems using statistical mechanics we propose an ensemble that lies in between the familiar canonical and microcanonical ensembles. From a comparative study of these ensembles we conclude that…
Small thermodynamic systems exhibit peculiar behavior different from that observed in long-scale systems. Non-equilibrium processes taking place in those systems are strongly influenced by the presence of fluctuations which can be large.…
Employing physically-consistent numerical methods is an important step towards attaining robust and accurate numerical simulations. When addressing compressible flows, in addition to preserving kinetic energy at a discrete level, as done in…
We investigate the geometric properties of the equilibrium manifold of a thermodynamic system determined by the van der Waals equations of state. We use the formalism of geometrothermodynamics to obtain results that are invariant under…
The microscopic structure of several amorphous substances often reveals complex patterns such as medium- or long-range order, spatial heterogeneity, and even local polycrystallinity. To capture all these features, models usually incorporate…
A novel geometric formalism for statistical estimation is applied here to the canonical distribution of classical statistical mechanics. In this scheme thermodynamic states, or equivalently, statistical mechanical states, can be…
Inherent structure theory is used to discover strong connections between simple characteristics of protein structure and the energy landscape of a Go model. The potential energies and vibrational free energies of inherent structures are…
The thermodynamics of ideal gas on the noncommutative geometry in the coherent state formalism is investigated. We first evaluate the statistical interparticle potential and see that there are residual "attraction (repulsion) potential"…
We study a microscopically realistic model of a physical gel and use computer simulations to investigate its static and dynamic properties at thermal equilibrium. The phase diagram comprises a sol phase, a coexistence region ending at a…
The problem of the calculation of equilibrium thermodynamic properties and the establishment of statistical-thermodynamically-consistent finite bound-state partition functions in nonideal multi-component plasma systems is revised within the…
All current formulations of nonequilibrium thermodynamics of open chemical reaction networks rely on the assumption of non-interacting species. We develop a general theory which accounts for interactions between chemical species within a…
Machine learning techniques are being increasingly used as flexible non-linear fitting and prediction tools in the physical sciences. Fitting functions that exhibit multiple solutions as local minima can be analysed in terms of the…