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At temperatures well above the transition, QCD admits a thermally reduced version in 3D, which reproduces the long distance physics. We analyze the phase diagram, point out the relevance of Z(3) symmetry in the location of the transition…
This paper prescribes a distance between learning tasks modeled as joint distributions on data and labels. Using tools in information geometry, the distance is defined to be the length of the shortest weight trajectory on a Riemannian…
Surface tension of small grains and droplets makes them stable only at a much lower temperature than in bulk. This makes spontaneous nucleation unfavorable in many cases. Kinetic approaches are delicate in that one can easily generate…
A new theory on gas-liquid phase transition is given. The new idea is that the total intermolecular potential energy for a classical system in equilibrium is relative with the average distance of molecules. A new space homogeneity…
The liquid-gas transition in free atomic clusters is investigated theoretically based on simple unimolecular rate theories and assuming sequential evaporations. A kinetic Monte Carlo scheme is used to compute the time-dependent properties…
Microcanonical thermodynamics (MT) is analysed for phase transitions of first and second order in finite systems. The transiton temperature, the latent heat and the surface tension of first order transitions can easily be determined by MT…
Topological Data Analysis methods can be useful for classification and clustering tasks in many different fields as they can provide two dimensional persistence diagrams that summarize important information about the shape of potentially…
Geodesic distance serves as a reliable means of measuring distance in nonlinear spaces, and such nonlinear manifolds are prevalent in the current multimodal learning. In these scenarios, some samples may exhibit high similarity, yet they…
If the structure of spacetime is discrete, then Lorentz symmetry should only be an approximation, valid at long length scales. At finite lattice spacings there will be small corrections to the Dirac evolution that could in principle be…
By combining different ideas, a general and efficient protocol to deal with discontinuous phase transitions at low temperatures is proposed. For small $T$'s, it is possible to derive a generic analytic expression for appropriate order…
Using contact geometry we give a new characterization of a simple but important class of thermodynamical systems which naturally satisfy the first law of thermodynamics (total energy preservation) and the second law (increase of entropy).…
Single-cell omics enable the profiles of cells, which contain large numbers of biological features, to be quantified. Cluster analysis, a dimensionality reduction process, is used to reduce the dimensions of the data to make it…
We present a detailed derivation of a microscopic theory for the glass transition of a liquid enclosed between two parallel walls relying on a mode-coupling approximation. This geometry lacks translational invariance perpendicular to the…
Two-dimensional (2D) particulate aggregates formed due to competing interactions exhibit a range of non-equilibrium steady state morphologies from finite-size compact crystalline structures to non-compact string-like conformations. We…
We develop a transitional geometry, that is, a family of geometries of constant curvatures which makes a continuous connec-tion between the hyperbolic, Euclidean and spherical geometries. In this transitional setting, several geometric…
Despite the simplicity of its molecular unit, water is a challenging system because of its uniquely rich polymorphism and predicted but yet unconfirmed features. Introducing a novel space of generalized coordinates that capture changes in…
Transitions of many-particle quantum systems between distinct phases at absolute-zero temperature, known as quantum phase transitions, require an exacting treatment of particle correlations. In this work, we present a general…
Geometrical approach to the phenomenological theory of phase transitions of the second kind at constant pressure $P$ and variable temperature $T$ is proposed. Equilibrium states of a system at zero external field and fixed $P$ and $T$ are…
We introduce the heat method for computing the shortest geodesic distance to a specified subset (e.g., point or curve) of a given domain. The heat method is robust, efficient, and simple to implement since it is based on solving a pair of…
We describe the Hamilton geometry of the phase space of particles whose motion is characterised by general dispersion relations. In this framework spacetime and momentum space are naturally curved and intertwined, allowing for a…