Entropy drives the phase behavior of colloids ranging from dense suspensions of hard spheres or rods to dilute suspensions of hard spheres and depletants. Entropic ordering of anisotropic shapes into complex crystals, liquid crystals, and even quasicrystals was demonstrated recently in computer simulations and experiments. The ordering of shapes appears to arise from the emergence of directiona...

We derive an upper bound for the mean of the supremum of the empirical process indexed by a class of functions that are known to have variance bounded by a small constant δ. The bound is expressed in the uniform entropy integral of the class at δ. The bound yields a rate of convergence of minimum contrast estimators when applied to the modulus of continuity of the contrast functions.

Traditional detectors for spectrum sensing in cognitive radio networks always become disabled when noise uncertainty is severe. Shannon entropy-based detection methods have aroused widespread attention in recent years due to the characteristics of effective anti-noise uncertainty. However, in existing entropy-based sensing schemes, the uniform quantization method cannot guarantee the maximum en...

We introduce the term smooth entanglement entropy transfer, a phenomenon that is a consequence of the causality-cancellation property of the quantum gravity environment. The causality-cancellation of the quantum gravity space removes the causal dependencies of the local systems. We study the physical effects of the causality-cancellation and show that it stimulates entropy transfer between the ...

The height of an algebraic number in the sense of Diophantine geometry is a measure of arithmetic complexity. There is a well-known relationship between the entropy of automorphisms of solenoids and classical heights. We consider an elliptic analogue of this relationship, which involves two novel features. Firstly, the introduction of a notion of entropy for sequences of transformations. Second...

The height of an algebraic number in the sense of Diophantine geometry is known to be related to the entropy of an automorphism of a solenoid associated to the number. An el-liptic analogue is considered, which necessitates introducing a notion of entropy for sequences of transformations. A sequence of transformations are defined for which there is a canonical arithmetically defined quotient wh...

We derive differential equations for the flow of entanglement entropy as a function of the metric and the couplings of the theory. The variation of the universal part of entanglement entropy under a local Weyl transformation is related to the variation under a local change in the couplings. We show that this relation is in fact equivalent to the trace Ward identity. As a concrete application of...

We refine an abstract result of the authors [JP3] concerning the strict positivity of entropy production of L1–asymptotically Abelian C∗-dynamical systems and apply the new result to a model describing finitely many free Fermi gas reservoirs coupled by local interactions. In particular, assuming that the reservoirs are initially not at equal temperatures or chemical potentials, we show that the...

We prove that for a class of Zd shifts of finite type, d > 1, any invariant measure which is not a measure of maximal entropy can be perturbed a small amount in the weak* topology to an invariant measure of higher entropy. Namely, there are no invariant measures which are strictly local maxima for the entropy function.

One can identify the number density of the microscopic space–time degrees of freedom in any diffeomorphism-invariant theory of gravity by using the principle of equipartition, applied to the area elements of a surface ∂V which are at the local Unruh temperature. The entropy associated with these degrees of freedom, which matches with the Wald entropy for the theory, can be used to obtain the fi...