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Gravity is a macroscopic manifestation of a microscopic quantum theory of space-time, just as the theories of elasticity and hydrodynamics are the macroscopic manifestation of the underlying quantum theory of atoms. The connection of…
We study the evolution of Tsallis entropy along the heat flow and establish its concavity in arbitrary dimensions. Extending prior results that were restricted to the one-dimensional setting, we prove that the Tsallis entropy is concave in…
We introduce a systematic classification method for the analogs of phase transitions in finite systems. This completely general analysis, which is applicable to any physical system and extends towards the thermodynamic limit, is based on…
The traditional dynamical phase transition refers to the appearance of singularities in an observable with respect to a control parameter for a late-time state or singularities in the rate function of the Loschmidt echo with respect to…
We investigate the scaling of the bipartite entanglement entropy across Lifshitz quantum phase transitions, where the topology of the Fermi surface changes without any changes in symmetry. We present both numerical and analytical results…
Entanglement entropies have revealed, in the last years, to be a powerful tool to extract information about the physics of condensed-matter systems. In the first part of this thesis, we show how to extract essential details about the…
Entropy is a quantity for counting physical degrees of freedom in a system. At a finite temperature, one can use thermal entropy to study thermodynamical properties. At zero temperature, entanglement entropy is expected to provide a…
An explosive percolation transition is the abrupt emergence of a giant cluster at a threshold caused by a suppression of the growth of large clusters. In this paper, we consider the information entropy of the cluster size distribution,…
In this paper, we discuss the connection between two genuinely quantum phenomena --- the discontinuity of quantum maximum entropy inference and quantum phase transitions at zero temperature. It is shown that the discontinuity of the maximum…
We investigate the behavior of entanglement entropy in the holographic QCD model proposed by Gubser et al. By choosing suitable parameters of the scalar self-interaction potential, this model can exhibit various types of phase structures:…
Given a factor code $\pi$ from a one-dimensional shift of finite type $X$ onto an irreducible sofic shift $Y$, if $\pi$ is finite-to-one there is an invariant called the degree of $\pi$ which is defined the number of preimages of a typical…
From the microscopic point of view almost all bonds between particles of condensed substances must be performed by exchanges of virtual photons. Consequently the duration of their virtuality must be longer than the extent of their free path…
A molecular theory of the glass transition of network forming liquids is developed using a combination of self-consistent phonon and liquid state approaches. Both the dynamical transition and the entropy crisis characteristic of random…
The principle of entropy increase is not only the basis of statistical mechanics, but also closely related to the irreversibility of time, the origin of life, chaos and turbulence. In this paper, we first discuss the dynamic system…
A nonextensive thermostatic approach to chaotic dynamical systems is developed by expressing generalized Tsallis distribution as escort distribution. We explicitly show the thermodynamic limit and also derive the Legendre Transform…
Entanglement entropy in topologically ordered matter phases has been computed extensively using various methods. In this paper, we study the entanglement entropy of topological phases in two-spaces from a new perspective---the perspective…
Astrophysical transient phenomena are traditionally classified spectroscopically in a hierarchical taxonomy; however, this graph structure is currently not utilized in neural net-based photometric classifiers for time-domain astrophysics.…
Symbolic sequences with long-range correlations are expected to result in a slow regression to a steady state of entropy increase. However, we prove that also in this case a fast transition to a constant rate of entropy increase can be…
Consider an ergodic measure preserving dynamical system $(T,X,\mu)$, and an observable $\phi:X\to\mathbb{R}$. For the time series $X_n(x)=\phi(T^{n}(x))$, we establish limit laws for the maximum process $M_n=\max_{k\leq n}X_k$ in the case…
The principle of maximum entropy is a broadly applicable technique for computing a distribution with the least amount of information possible while constrained to match empirically estimated feature expectations. However, in many real-world…