scholarly journals Systems with almost specification property may have zero entropy

2015 ◽  
Vol 31 (2) ◽  
pp. 228-235
Author(s):  
Yiwei Dong
2010 ◽  
Vol 31 (1) ◽  
pp. 49-75 ◽  
Author(s):  
E. GLASNER ◽  
M. LEMAŃCZYK ◽  
B. WEISS

AbstractWe introduce a functor which associates to every measure-preserving system (X,ℬ,μ,T) a topological system $(C_2(\mu ),\tilde {T})$ defined on the space of twofold couplings of μ, called the topological lens of T. We show that often the topological lens ‘magnifies’ the basic measure dynamical properties of T in terms of the corresponding topological properties of $\tilde {T}$. Some of our main results are as follows: (i) T is weakly mixing if and only if $\tilde {T}$ is topologically transitive (if and only if it is topologically weakly mixing); (ii) T has zero entropy if and only if $\tilde {T}$ has zero topological entropy, and T has positive entropy if and only if $\tilde {T}$ has infinite topological entropy; (iii) for T a K-system, the topological lens is a P-system (i.e. it is topologically transitive and the set of periodic points is dense; such systems are also called chaotic in the sense of Devaney).


2021 ◽  
Vol 2021 (5) ◽  
Author(s):  
Jie Ren

Abstract We analytically study phase transitions of holographic charged Rényi entropies in two gravitational systems dual to the $$ \mathcal{N} $$ N = 4 super-Yang-Mills theory at finite density and zero temperature. The first system is the Reissner-Nordström-AdS5 black hole, which has finite entropy at zero temperature. The second system is a charged dilatonic black hole in AdS5, which has zero entropy at zero temperature. Hyperbolic black holes are employed to calculate the Rényi entropies with the entangling surface being a sphere. We perturb each system by a charged scalar field, and look for a zero mode signaling the instability of the extremal hyperbolic black hole. Zero modes as well as the leading order of the full retarded Green’s function are analytically solved for both systems, in contrast to previous studies in which only the IR (near horizon) instability was analytically treated.


2015 ◽  
Vol 3 (1) ◽  
Author(s):  
Brendan Goldsmith ◽  
Ketao Gong

AbstractNecessary and sufficient conditions to ensure that the direct sum of two Abelian groups with zero entropy is again of zero entropy are still unknown; interestingly the same problem is also unresolved for direct sums of Hopfian and co-Hopfian groups.We obtain sufficient conditions in some situations by placing restrictions on the homomorphisms between the groups. There are clear similarities between the various cases but there is not a simple duality involved.


1996 ◽  
Vol 16 (2) ◽  
pp. 379-404 ◽  
Author(s):  
Thierry De La Rue

AbstractWe construct two real Gaussian dynamical systems of zero entropy; the first one is not loosely Bernoulli, and the second is a loosely Bernoulli Gaussian-Kronecker system. To get loose-Bernoullicity for the second system, we prove and use a property of planar Brownian motion on [0, 1]: we can recover the whole trajectory knowing only some angles formed by the motion.


2020 ◽  
Author(s):  
kazimieras Tamoliūnas ◽  
Nuno Galamba

The hydrophobic effect plays a key role in many chemical and biological processes, including protein folding. Nonetheless, a comprehensive picture of the effect of temperature on hydrophobic hydration and protein denaturation remains elusive. Here, we study the effect of temperature on the hydration of model hydrophobic and amphiphilic solutes through molecular dynamics aiming at getting in sight on the singular behavior of water concerning the zero entropy temperature TS and entropic convergence also observed upon protein denaturation. We show that, similar to hydrocarbons and proteins, polar amphiphilic solutes exhibit a TS, although strongly dependent upon solute-water interactions, opposite to hydrocarbons. Further, the temperature dependence of the hydration entropy normalized by the solvent accessible surface area is shown to be nearly solute size independent for hydrophobic but not for amphiphilic solutes, for similar reasons. These results are further discussed in the light of information theory (IT) and the structure of water around hydrophobic groups The latter shows that the tetrahedral enhancement of some water molecules around hydrophobic groups, associated with the reduction of water defects, leads to the strengthening of the weakest hydrogen bonds, relative to bulk water. However, a larger tetrahedrality is found in low density water populations, demonstrating that pure water has encoded structural information similar to that associated with hydrophobic hydration, consistent with IT assumptions. The source of the differences between Kauzmann's "hydrocarbon model" on protein denaturation and hydrophobic hydration is also discussed with relatively large amphiphilic hydrocarbons displaying a more similar behavior to globular proteins, than aliphatic hydrocarbons.<br>


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