Related papers: Phase Transitions as Emergent Geometric Phenomena:…
Inspired by "quantum graphity" models for spacetime, a statistical model of graphs is proposed to explore possible realizations of emergent manifolds. Graphs with given numbers of vertices and edges are considered, governed by a very…
Newtonian dynamics is derived from prior information codified into an appropriate statistical model. The basic assumption is that there is an irreducible uncertainty in the location of particles so that the state of a particle is defined by…
There is an ever-growing need for predictive models for the elasto-viscoplastic deformation of solids. Our goal in this paper is to incorporate recently developed out-of-equilibrium statistical concepts into a thermodynamically consistent,…
Phase transitions impose topological constraints on thermodynamic state variables, masking energetic fluctuations at the phase boundary. This constraint is most apparent in melting systems, where temperature remains pinned despite continued…
The ground states of noninteracting fermions in one-dimension with chiral symmetry form a class of topological band insulators, described by a topological invariant that can be related to the Zak phase. Recently, a generalization of this…
The stationary points of the potential energy function V are studied for the \phi^4 model on a two-dimensional square lattice with nearest-neighbor interactions. On the basis of analytical and numerical results, we explore the relation of…
Individual phases are commonly considered as the building blocks of materials. However, the accurate theoretical prediction of properties of individual phases remains elusive. The top-down approach by decoding genomic building blocks of…
Because only two variables are needed to characterize a simple thermodynamic system in equilibrium, any such system is constrained on a 2D manifold. Of particular interest are the exact 1-forms on the cotangent space of that manifold, since…
On the basis of information theory, a new formalism of classical non-relativistic mechanics of a mass point is proposed. The particle trajectories of a general dynamical system defined on an (1+n)-dimensional smooth manifold are treated…
We develop a comprehensive cosmological framework based on the principle that our universe originated as a three-dimensional spatial configuration governed purely by energy functionals, with time emerging dynamically through quantum loop…
Thermodynamic relations are derived from first principles of mechanics for non-equilibrium processes. Since the key role herein is played by the law of increase of entropy, the latter is analyzed at first. It is shown that its derivation…
We present a class of thermodynamic systems with constant thermodynamic curvature which, within the context of geometric approaches of thermodynamics, can be interpreted as constant thermodynamic interaction among their components. In…
Since Newton, all classical and quantum physics depends upon the "Newtonian Paradigm". Here the relevant variables of the system are identified. The boundary conditions creating the phase space of all possible values of the variables are…
By viewing entanglement as a state function, a new kind of phase transition takes place: the geometric phase transition. This phenomenon occurs due to singularities in the shape of the entangled states set. It is shown how this result can…
This paper is a review of results which have been recently obtained by applying mathematical concepts drawn, in particular, from differential geometry and topology, to the physics of Hamiltonian dynamical systems with many degrees of…
We introduce a universal criterion for criticality in mean-field rotor Hamiltonians based on the geometric structure of the constant-energy shell. Rather than characterizing the onset of a phase transition through the conventional…
We show that, when we study the coexistence of general relativity with thermodynamics, some physical properties that are usually thought of as holographic and lying in the domain of quantum gravity can actually be accessed even at the…
In this Letter we study interacting systems with spontaneous discrete symmetry breaking, where the degenerate symmetry-broken states are topologically distinct gapped phases. Edge modes appear at domain walls between the two topological…
Clustering $\unicode{x2013}$ the tendency for neighbors of nodes to be connected $\unicode{x2013}$ quantifies the coupling of a complex network to its latent metric space. In random geometric graphs, clustering undergoes a continuous phase…
Near Horizon Extremal Geometries (NHEG), are geometries which may appear in the near horizon region of the extremal black holes. These geometries have $SL(2,\mathbb{R})\!\times\!U(1)^n$ isometry, and constitute a family of solutions to the…