Related papers: Failure of the Volume Function in Granular Statist…
Thermal fluctuations are not large enough to lead to state changes in granular materials. However, such materials do achieve reproducible bulk properties, suggesting that they are controlled by an underlying statistical mechanics analogous…
We construct a new mesoscopic model for granular media using Dynamical Density Functional Theory (DDFT). The model includes both a collision operator to incorporate inelasticity and the Helmholtz free energy functional to account for…
Entropy of matter in a very strong gravity depends on cross-sectional area of the container of the system -- is being further bolstered by calculating entropy of a monoatomic gas kept under uniform strong gravity at Newtonian scale. This…
We simulate via a Discrete Element Method the tapping of a narrow column of disk under gravity. For frictionless disks, this system has a simple analytic expression for the density of states in the Edwards volume ensemble. We compare the…
Time-reversal symmetry breaking and entropy production are universal features of nonequilibrium phenomena. Despite its importance in the physics of active and living systems, the entropy production of systems with many degrees of freedom…
The paper describes an approach to measuring convergence of an algorithm to its result in terms of an entropy-like function of partitions of its inputs of a given length. The goal is to look at the algorithmic data processing from the…
Nonextensive Statistical Mechanics has developed into an important framework for modeling the thermodynamics of complex systems and the information of complex signals. Upon the 80th birthday of the field's founder, Constantino Tsallis, a…
Understanding the core content of quantum mechanics requires us to disentangle the hidden logical relationships between the postulates of this theory. Here we show that the mathematical structure of quantum measurements, the formula for…
Nanoscale machines are strongly influenced by thermal fluctuations, contrary to their macroscopic counterparts. As a consequence, even the efficiency of such microscopic machines becomes a fluctuating random variable. Using geometric…
In this paper we develop a general formalism of a path approach for non-equilibrium statistical mechanics. Firstly, we consider the classical Gibbs approach for states and find that this formalism is ineffective for non-equilibrium…
The first aims of this work are to endorse the advent of finitely additive set functions as equilibrium states and the possibility to replace the metric entropy by an upper semi-continuous map associated to a general variational principle.…
Naturally-occurring granular materials often consist of angular particles whose shape and frictional characteristics may have important implications on macroscopic flow rheology. In this paper, we provide a theoretical account for the…
The concept of depth has proved very important for multivariate and functional data analysis, as it essentially acts as a surrogate for the notion a ranking of observations which is absent in more than one dimension. Motivated by the rapid…
The notion of probability density for a random function is not as straightforward as in finite-dimensional cases. While a probability density function generally does not exist for functional data, we show that it is possible to develop the…
Devising a statistical mechanics framework for jammed granular materials is a challenging task as those systems do not share some important properties required to characterize them with statistical thermodynamics tools. In a recent paper…
We considered the thermodynamics in spaces with deformed commutation relation leading to existence of the minimal length. We developed a classical method of the partition function evaluation. We calculated the partition function and heat…
Entropy can signify different things: For instance, heat transfer in thermodynamics or a measure of information in data analysis. Many entropies have been introduced and it can be difficult to ascertain their different importance and…
Non-orthogonality errors in unstructured Finite Volume methods for simulating incompressible two-phase flows may break the force-balanced discretization. We show that applying the same explicit non-orthogonality correction for all gradient…
The volume fluctuations in the steady state reached by a vibrated granular gas of hard particles confined by a movable piston on the top are investigated by means of event driven simulations. Also, a compressibility factor, measuring the…
A novel powerful mathematical method is presented, which allows us to find an analytical solution of a simplified version of the statistical multifragmentation model with the restriction that the largest fragment size cannot exceed the…