相关论文: Riemannian submersions for q-entropies

Entropy is a fundamental concept in equilibrium statistical mechanics, yet its origin in the non-equilibrium dynamics of isolated quantum systems is not fully understood. A strong consensus is emerging around the idea that the stationary…

Entanglement measures such as the entanglement entropy have become an indispensable tool to identify the fundamental character of ground states of interacting quantum many-body systems. For systems of interacting spin or bosonic degrees of…

We consider the description of open quantum systems with probability sinks (or sources) in terms of general non-Hermitian Hamiltonians.~Within such a framework, we study novel possible definitions of the quantum linear entropy as an…

We study the problem of detecting the structure of a complex dynamical system described by a set of deterministic differential equation that contains a Hamiltonian subsystem, without any information on the explicit form of evolution laws.…

The state of a thermodynamic system being characterized by its set of extensive variables $q^{i}(i=1,...,n) ,$ we write the associated intensive variables $\gamma_{i},$ the partial derivatives of the entropy $ S(q^{1},...,q^{n}) \equiv…

A description of Lagrangian and Hamiltonian formalisms naturally arisen from the invariance structure of given nonlinear dynamical systems on the infinite--dimensional functional manifold is presented. The basic ideas used to formulate the…

Information-theoretic quantities such as Renyi entropies show a remarkable universality in their late-time behaviour across a variety of chaotic many-body systems. Understanding how such common features emerge from very different…

This essay advocates the view that any problem that has a meaningful empirical content, can be formulated in constructive, more definitely, finite terms. We consider combinatorial models of dynamical systems and approaches to statistical…

We combine an axiomatics of R\'{e}nyi with the $q$--deformed version of Khinchin axioms to obtain a measure of information (i.e., entropy) which accounts both for systems with embedded self-similarity and non-extensivity. We show that the…

Based on the q-exponential distribution which has been observed in more and more physical systems, the varentropy method is used to derive the uncertainty measure of such an abnormal distribution function. The uncertainty measure obtained…

The computational challenges posed by many-particle quantum systems are often overcome by mixed quantum-classical (MQC) models in which certain degrees of freedom are treated as classical while others are retained as quantum. One of the…

The variational method is very important in mathematical and theoretical physics because it allows us to describe the natural systems by physical quantities independently from the frame of reference used. A global and statistical approach…

It has been argued in [EPL {\bf 90} (2010) 50004], entitled {\it Essential discreteness in generalized thermostatistics with non-logarithmic entropy}, that "continuous Hamiltonian systems with long-range interactions and the so-called…

Using arguments built on ergodicity, we derive an analytical expression for the Renyi entanglement entropies corresponding to the finite-energy density eigenstates of chaotic many-body Hamiltonians. The expression is a universal function of…

The fact that a temperature and an entropy may be associated with horizons in semi-classical general relativity has led many to suspect that spacetime has microstructure. If this is indeed the case then its description via Riemannian…

A general investigation is made into the intrinsic Riemannian geometry for complex systems, from the perspective of statistical mechanics. The entropic formulation of statistical mechanics is the ingredient which enables a connection…

Entropic Dynamics is a framework in which dynamical laws are derived as an application of entropic methods of inference. No underlying action principle is postulated. Instead, the dynamics is driven by entropy subject to the constraints…

In this paper we first propose a framework of structure-preserving submersions, which generalises the concept of a Riemannian submersion, and dualises the concept of subgeometry, or "structure-preserving immersions". The emphasis of our…

After a brief introduction to the concept of entanglement in quantum systems, I apply these ideas to many-body systems and show that the von Neumann entropy is an effective way of characterising the entanglement between the degrees of…

We employ the quasiparticle picture of entanglement evolution to obtain an effective description for the out-of-equilibrium Entanglement Hamiltonian at the hydrodynamical scale following quantum quenches in free fermionic systems in two or…