Related papers: Continuity properties of folding entropy
The presence of defects in solids formed by active particles breaks their discrete translational symmetry. As a consequence, many of their properties become space-dependent and different from those characterizing perfectly ordered…
We establish strong Feller property and irreducibility for the transition semigroup associated to a class of nonlinear stochastic partial differential equations with multiplicative degenerate noise. As a by-product, we prove uniqueness of…
The fluctuation theorem for entropy production is a remarkable symmetry of the distribution of produced entropy that holds universally in non-equilibrium steady states with Markovian dynamics. However, in systems with slow degrees of…
We introduce a simple geometrical construction similar to covariant holographic entanglement entropy but with the addition of a new term proportional to boundary region volume. This new procedure has properties strongly resembling classical…
There is a relation between the irreversibility of thermodynamic processes as expressed by the breaking of time-reversal symmetry, and the entropy production in such processes. We explain on an elementary mathematical level the relations…
For deterministic continuous time nonlinear control systems, epsilon-practical stabilization entropy and practical stabilization entropy are introduced. Here the rate of attraction is specified by a KL-function. Upper and lower bounds for…
Linearity of a dynamical entropy means that the dynamical entropy of the n-fold composition of a dynamical map with itself is equal to n times the dynamical entropy of the map for every positive integer n. We show that the quantum dynamical…
Product shape is one of the factors that trigger preference decisions of customers. Congruity of shape elements and deformation of shape from the prototype are two factors that are found to influence aesthetic response, hence preference. We…
We propose a housekeeping/excess decomposition of entropy production for general nonlinear dynamics in a discrete space, including chemical reaction networks and discrete stochastic systems. We exploit the geometric structure of…
We prove existence of the largest entropy sub-solution and the smallest entropy super-solution to the Cauchy problem for a nonlinear degenerate parabolic equation with only continuous flux and diffusion functions. Applying this result, we…
Thermodynamic extensivity is commonly introduced as a postulate -- the homogeneity of degree one in thermodynamic potentials. We provide a constructive derivation of this property from microscopic conditions on the pair potential, without…
Entropy metrics (for example, permutation entropy) are nonlinear measures of irregularity in time series (one-dimensional data). Some of these entropy metrics can be generalised to data on periodic structures such as a grid or lattice…
We consider a free-fermion chain with a conformal defect that features an extended zero mode, and study the entanglement properties in its mixed ground state. The zero-mode induced degeneracy modifies the density of states in the…
We use gauge-gravity duality to compute entanglement entropy in a non-conformal background with an energy scale $\Lambda$. At zero temperature, we observe that entanglement entropy decreases by raising $\Lambda$. However, at finite…
The characterization of irreversibility in general quantum processes is an open problem of increasing techno- logical relevance. Yet, the tools currently available to this aim are mostly limited to the assessment of dynamics induced by…
Non-reciprocal interactions are present in many systems out of equilibrium. The rate of entropy production is a measure that quantifies the time irreversibility of a system, and thus how far it is from equilibrium. In this work, we…
The notion of entropy appears in many fields and this paper is a survey about entropies in several branches of Mathematics. We are mainly concerned with the topological and the algebraic entropy in the context of continuous endomorphisms of…
Given a compact topological dynamical system (X, f) with positive entropy and upper semi-continuous entropy map, and any closed invariant subset $Y \subset X$ with positive entropy, we show that there exists a continuous roof function such…
In this paper, we study the entanglement entropy of a single interval on a cylinder in two-dimensional $T\overline{T}$-deformed conformal field theory. For such case, the (R\'enyi) entanglement entropy takes a universal form in a CFT. We…
Today's thermodynamics is largely based on the combined law for equilibrium systems and statistical mechanics derived by Gibbs in 1873 and 1901, respectively, while irreversible thermodynamics for nonequilibrium systems resides essentially…