相关论文: Entropy loss in long-distance DNA looping
We study the ground state entanglement entropy of the quantum Dyson hierarchical spin chain in which the interaction decays algebraically with the distance as $r^{-1-\sigma}$. We exploit the real-space renormalisation group solution which…
Dilatations by means of a constant factor can be seen in a double way: as a simple change of units length or as a conformal mapping of the starting spacetime into a ``stretched'' one with the same units length. The numerical value of the…
We report a theoretical study of DNA flexibility and quantitatively predict the ring closure probability as a function of DNA contour length. Recent experimental studies show that the flexibility of short DNA fragments (as compared to the…
We report model calculations on DNA single strands which describe the equilibrium dynamics and kinetics of hairpin formation and melting. Modeling is at the level of single bases. Strand rigidity is described in terms of simple polymer…
It is shown that the residual entropy (entropy minus that of the ideal gas at the same temperature and density) is mostly synonymous with the independent variable of density scaling, identifying a direct link between these two approaches.…
We calculate the conductance of atomic chains as a function of their length. Using the Density Matrix Renormalization Group algorithm for a many-body model which takes into account electron-electron interactions and the shape of the…
Loop formation between monomers in the interior of semiflexible chains describes elementary events in biomolecular folding and DNA bending. We calculate analytically the interior distance distribution function for semiflexible chains using…
A general upper bound for topological entropy of switched nonlinear systems is constructed, using an asymptotic average of upper limits of the matrix measures of Jacobian matrices of strongly persistent individual modes, weighted by their…
Whether a system is to be considered complex or not depends on how one searches for correlations. We propose a general scheme for calculation of entropies in lattice systems that has high flexibility in how correlations are successively…
Large reasoning models have demonstrated remarkable performance on complex reasoning tasks, yet the excessive length of their chain-of-thought outputs remains a major practical bottleneck due to high computation cost and poor deployability.…
The tight, in a sense, lower estimates of diamond-norm distance from a given quantum channel to the sets of degradable, antidegradable and entanglement-breaking channels are obtained via the tight continuity bounds for quantum mutual…
The cross-entropy scaling law has long served as a key tool for guiding the development of large language models. It shows that cross-entropy loss decreases in a predictable power-law rate as the model size increases. However, recent…
We study the entropy of the set traced by an $n$-step random walk on $\Z^d$. We show that for $d \geq 3$, the entropy is of order $n$. For $d = 2$, the entropy is of order $n/\log^2 n$. These values are essentially governed by the size of…
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…
We consider the task of deriving a key with high HILL entropy from an unpredictable source. Previous to this work, the only known way to transform unpredictability into a key that was $\eps$ indistinguishable from having min-entropy was via…
Over the past years, the ever-growing trend on data storage demand, more specifically for "cold" data (i.e. rarely accessed), has motivated research for alternative systems of data storage. Because of its biochemical characteristics,…
We examine the elastic model of short circular DNA. We obtain analytic expressions for configurations, elastic energy, twist and linking number of our solutions. We find the onset of the plectonemic transition. We suggest ways to use our…
The entanglement entropy of an annulus is examined in a three-dimensional system with or without a gap. For a free massive scalar field theory, we numerically calculate the mutual information across an annulus. We also study the holographic…
We investigate the longest common substring problem for encoded sequences and its asymptotic behaviour. The main result is a strong law of large numbers for a re-scaled version of this quantity, which presents an explicit relation with the…
Distribution of loops in a one-dimensional random walk (RW), or, equivalently, neutral segments in a sequence of positive and negative charges is important for understanding the low energy states of randomly charged polymers. We investigate…