Related papers: Residual Entropy of Ice: A Study Based on Transfer…
'Causal' direction is of great importance when dealing with complex systems. Often big volumes of data in the form of time series are available and it is important to develop methods that can inform about possible causal connections between…
We define the projected entropy S(T) at a given temperature T in the context of an Ising model transition matrix calculation as the entropy associated with the distribution of Markov chain realizations in energy-magnetization, E-H, space.…
Ice Ih, the common form of ice in the biosphere, contains proton disorder. Its proton-ordered counterpart, ice XI, is thermodynamically stable below 72 K. However, even below this temperature the formation of ice XI is kinetically hindered…
Nonlinear feedbacks in the Earth System provide mechanisms that can prove very useful in understanding complex dynamics with relatively simple concepts. For example, the temperature and the ice cover of the planet are linked in a positive…
This study provides a comprehensive analysis of the ground state and thermodynamic properties of a spin-pseudospin chain representing a model of a one-dimensional dilute magnet with two types of nonmagnetic charged impurities. For this…
In any Markov chain with finite state space the distribution of transition records always belongs to the exponential family. This observation is used to prove a fluctuation theorem, and to show that the dynamical entropy of a stationary…
We consider the Ising model on the hexagonal lattice evolving according to Metropolis dynamics. We study its metastable behavior in the limit of vanishing temperature when the system is immersed in a small external magnetic field. We…
We present a set of cluster models that link the present-day properties of clusters to the processes that govern galaxy formation. These models treat the entropy distribution of the intracluster medium as its most fundamental property.…
Classical particle systems characterized by continuous size polydispersity, such as colloidal materials, are not straightforwardly described using statistical mechanics, since fundamental issues may arise from particle distinguishability.…
A method is proposed for exactly calculating the partition function of a rectangular Ising lattice with the presence of a uniform external field. This approach is based on the method of the transfer matrix developed about seventy years ago…
We explore the Iterative Inference Hypothesis (IIH) within the context of transformer-based language models, aiming to understand how a model's latent representations are progressively refined and whether observable differences are present…
Using transfer matrix and finite-size scaling methods, we study the thermodynamic behavior of a lattice gas with two kinds of particles on the square lattice. Only excluded volume interactions are considered, so that the model is athermal.…
It has been implicitly assumed that ices on grains in molecular clouds and proto planetary disks are formed by homogeneous layers regardless of their composition or crystallinity. To verify this assumption, we observed the H2O deposition…
Using molecular dynamics simulations we compute the elastic constants of ice I$_h$ for a set of 8 frequently used semi-empirical potentials for water, namely the rigid-molecule SPC/E, TIP4P, TIP4P2005, TIP4P/Ice and TIP5P models, the…
A new continuum-mechanical formulation is proposed which encompasses all material processes within and surrounding an ice sheet. Using this formulation, the balance of mass and free-surface relations for ice sheets are derived and…
We investigate ice polyamorphism in the context of the two-dimensional Mercedes-Benz model of water. We find a first-order phase transition between a crystalline phase and a high-density amorphous phase. Furthermore we find a reversible…
We consider a system of Ising spins s=1/2 with nonmagnetic impurities with charge associated with pseudospin S=1. The charge density is fixed pursuant to the concentration n. Analysis of the thermodynamic properties in the one-dimensional…
We use rigorous non-equilibrium thermodynamic arguments to prove (i) the residual entropy of any system is bounded below by the experimentally (calorimetrically) determined absolute temperature entropy, which itself is bounded below by the…
Mean field replica theory is employed to analyze the freezing transition of random heteropolymers comprised of an arbitrary number ($q$) of types of monomers. Our formalism assumes that interactions are short range and heterogeneity comes…
The structure of the recently identified metastable ice XVII, obtained by release of hydrogen from the C$_0$ D$_2$O-H$_2$ compound (filled ice), has been accurately measured by neutron powder diffraction. The diffraction pattern is indexed…