Related papers: Continuity properties of folding entropy
We consider a one-dimensional persisent random walk viewed as a deterministic process with a form of time reversal symmetry. Particle reservoirs placed at both ends of the system induce a density current which drives the system out of…
The notion of slow entropy, both upper and lower slow entropy, was defined by Katok and Thouvenot as a more refined measure of complexity for dynamical systems, than the classical Kolmogorov-Sinai entropy. For any subexponential rate…
Active matter systems operate far from equilibrium due to the continuous energy injection at the scale of constituent particles. At larger scales, described by coarse-grained models, the global entropy production rate S quantifies the…
We study the homogeneous Landau equation with Maxwell molecules and prove that the entropy production is non-increasing provided the directional temperatures are well-distributed and the solution admits a moment of order $\ell$, for some…
The ordinal approach to evaluate time series due to innovative works of Bandt and Pompe has increasingly established itself among other techniques of nonlinear time series analysis. In this paper, we summarize and generalize the theory of…
We generalize several results of the classical theory of Thermodynamic Formalism by considering a compact metric space $M$ as the state space. We analyze the shift acting on $M^\mathbb{N}$ and consider a general a-priori probability for…
The entropy production is one of the most essential features for systems operating out of equilibrium. The formulation for discrete-state systems goes back to the celebrated Schnakenberg's work and hitherto can be carried out when for each…
The time evolution of entanglement entropy in generic chaotic many-body systems has an effective description in terms of a minimal membrane, characterised by a tension function. For 2d CFTs, a degenerate tension function reproduces several…
In this paper, we consider certain partially hyperbolic diffeomorphisms with center of arbitrary dimension and obtain continuity properties of the topological entropy under $C^1$ perturbations. The systems considered have subexponential…
In this paper, we introduce topological entropy for dynamical systems generated by a single local homeomorphism (Deaconu-Renault systems). More precisely, we generalize Adler, Konheim, and McAndrew's definition of entropy via covers and…
In this paper, we extend the concept of generalized entropy to uniform spaces, allowing computations beyond metrizable settings. We apply this to parabolic dynamics - systems with a unique fixed point uniformly attracting all compact…
There are three ways to conceptualize entropy: entropy as an extensive thermodynamic quantity of physical systems (Clausius, Boltzmann, Gibbs), entropy as a measure for information production of ergodic sources (Shannon), and entropy as a…
Here we deconstruct, and then in a reasoned way reconstruct, the concept of "entropy of a system," paying particular attention to where the randomness may be coming from. We start with the core concept of entropy as a COUNT associated with…
In this paper, we develop the notion of entropy for uniform hypergraphs via tensor theory. We employ the probability distribution of the generalized singular values, calculated from the higher-order singular value decomposition of the…
de Sitter vacuum of nonconformal gauge theories is non-equilibrium, manifested by a nonvanishing rate of the comoving entropy production at asymptotically late times. This entropy production rate is related to the entanglement entropy of…
Different notions of entropy play a fundamental role in the classical theory of dynamical systems. Unlike many other concepts used to analyze autonomous dynamics, both measure-theoretic and topological entropy can be extended quite…
The irreversible currents and entropy production rate of a dilute colloidal suspension are calculated using the linear irreversible thermodynamics and the linear response theory. The \anomalous" or \hidden" entropy recently discussed in the…
We consider the numerical integration of conservation laws endowed with an entropy inequality and we study the residual of the scheme on this inequality, which represents the numerical entropy production. This idea has been introduced and…
This work analyzes different notions of entropy and its production in $ep$ and heavy-ion collisions, focusing on the early stages of the collision. To this end, the importance of phenomena such as quantum entanglement and decoherence in…
By suitable reformulations, we review the mathematical frameworks of six different approaches to the description of non-equilibrium dynamics with the purpose to set up a unified formulation of the Maximum Entropy Production (MEP) principle…