Related papers: Residual Entropy of Ice: A Study Based on Transfer…
Starting from Shannon's definition of dynamic entropy, we proposed a simple theory to describe the transition between different rare event related dynamic states in condensed matters, and used it to investigate high pressure ice VII.…
We shall deal with both the barotropic and the full compressible Euler system in multiple space dimensions. Both systems are particular examples of hyperbolic conservation laws. Whereas for scalar conservation laws there exists a well-known…
This paper is about analytic properties of single transfer matrices originating from general block-tridiagonal or banded matrices. Such matrices occur in various applications in physics and numerical analysis. The eigenvalues of the…
In our derivation of the second law of thermodynamics from the relation of adiabatic accessibility of equilibrium states we stressed the importance of being able to scale a system's size without changing its intrinsic properties. This…
Nuclear quantum effects lead to an anomalous shift of the volume of hexagonal ice; heavy ice has a larger volume than light ice. This anomaly in ice increases with temperature and persists in liquid water up to the boiling point. We study…
A central result that arose in applying information theory to the stochastic thermodynamics of nonlinear dynamical systems is the Information-Processing Second Law (IPSL): the physical entropy of the universe can decrease if compensated by…
The mixed spin-1/2 Ising model and spin-1 Blume-Capel model in an hexagonal nanowire structure under the presence of crystal field is considered. The free energy is obtained through the transfer matrix technique, which is solved…
We discuss the problem of proton motion in Hydrogen bond materials with special focus on ice. We show that phenomenological models proposed in the past for the study of ice can be recast in terms of microscopic models in close relationship…
For the first order transition of the Ising model below $T_c$, Isakov has proven that the free energy possesses an essential singularity in the applied field. Such a singularity in the control parameter, anticipated by condensation theory,…
This paper presents an {\it ab initio} derivation of the expression given by irreversible thermodynamics for the rate of entropy production for different classes of diffusive processes. The first class are Lorentz gases, where…
The mathematical analysis on the behavior of the entropy for viscous, compressible, and heat conducting magnetohydrodynamic flows near the vacuum region is a challenging problem as the governing equation for entropy is highly degenerate and…
Using the transfer matrix technique, we estimate the entropy for a gas of rods of sizes equal to k (named k-mers), which cover completely a square lattice. Our calculations were made considering three different constructions, using…
Ice formation is ubiquitous in nature, with important consequences in a variety of environments, including biological cells, soil, aircraft, transportation infrastructure and atmospheric clouds. However, its intrinsic kinetics and…
The concept of entropy in nonequilibrium macroscopic systems is investigated in the light of an extended equation of motion for the density matrix obtained in a previous study. It is found that a time-dependent information entropy can be…
The thermodynamic definition of entropy can be extended to nonequilibrium systems based on its relation to information. To apply this definition in practice requires access to the physical system's microstates, which may be prohibitively…
A toy model of particles packings is presented, which consists in arranging hexagons on a triangular lattice according to local stability rules. The number of stable packings is analytically computed and found to grow exponentially with the…
The transfer-matrix methodology is used to solve linear systems of differential equations, such as those that arise when solving Schr\"odinger's equation, in situations where the solutions of interest are in the continuous part of the…
I study the physical nature of traces (or memories). Surprisingly, (i) systems separation with (ii) temperature differences and (iii) long thermalization times, are sufficient conditions to produce macroscopic traces. Traces of the past are…
A new graphical method is developed to calculate the critical temperature of 2- and 3-dimensional Ising models as well as that of the 2-dimensional Potts models. This method is based on the transfer matrix method and using the limited…
We carry out computer simulations of a simple, two-dimensional off-lattice model that exhibits inverse melting. The monodisperse system comprises core-softened disks interacting through a repulsive square shoulder located inside an…