Related papers: A Statistical-Physics Refinement of Soft Covering
A simple zipper model is introduced, representing in a simplified way, e.g., the folded DNA double helix or hairpin structures in RNA. The double stranded hairpin is connected to a heat bath at temperature $T$ and subject to an external…
We study the relaxation dynamics of a run and tumble particle in a one-dimensional piecewise linear potential $U(x)=b|x|$, from delta-function initial conditions at $x=0$ to steady state. In addition to experiencing active telegraphic…
We draw a certain analogy between the classical information-theoretic problem of lossy data compression (source coding) of memoryless information sources and the statistical mechanical behavior of a certain model of a chain of connected…
Phase separation plays an role in determining the self-assembly of biological and soft-matter systems. In biological systems, liquid-liquid phase separation inside a cell leads to the formation of various macromolecular aggregates. The…
The approach is developed for the description of isolated Fermi-systems with finite number of particles, such as complex atoms, nuclei, atomic clusters etc. It is based on statistical properties of chaotic excited states which are formed by…
In this PhD thesis, we explore and apply methods inspired by the free energy principle to two important areas in machine learning and neuroscience. The free energy principle is a general mathematical theory of the necessary…
For a finite random graph, we defined a simple model of statistical mechanics. We obtain an annealed asymptotic result for the random partition function for this model on finite random graphs as n; the size of the graph is very large. To…
We propose a method of characterizing radial networks based on a partition function associated with the structural triangulation of the network. The internal energy, Helmholtz free energy, and entropy derived from the partition function are…
Code Division Multiple Access (CDMA) in which the spreading code assignment to users contains a random element has recently become a cornerstone of CDMA research. The random element in the construction is particular attractive as it…
We determine the exact error and strong converse exponents of shared randomness-assisted channel simulation in worst case total-variation distance. Namely, we find that these exponents can be written as simple optimizations over the R\'enyi…
We derive a graph expansion for the thermal partition function of solvable two-dimensional models with boundaries. This expansion of the integration measure over the virtual particles winding around the time cycle is obtained with the help…
The present study focuses on direct numerical simulations of breaking waves generated by a wave plate at constant water depths. The aim is to quantify the dynamics and kinematics in the breaking process, together with the air entrainment…
We calculate exactly the first cumulants of the free energy of a directed polymer in a random medium for the geometry of a cylinder. By using the fact that the n-th moment <Z^n> of the partition function is given by the ground state energy…
We study the Stochastic Thermodynamics of cell growth and division using a theoretical framework based on branching processes with resetting. Cell division may be split into two sub-processes: branching, by which a given cell gives birth to…
We introduce a method to sample the orientational distribution function in computer simulations. The method is based on the exact torque balance equation for classical many-body systems of interacting anisotropic particles in equilibrium.…
We consider the hierarchic tree Random Energy Model with continuous branching and calculate the moments of the corresponding partition function. We establish the multifractal properties of those moments. We derive formulas for the normal…
Sparse Code Division Multiple Access (CDMA), a variation on the standard CDMA method in which the spreading (signature) matrix contains only a relatively small number of non-zero elements, is presented and analysed using methods of…
Stochastic chains represent a wide and key variety of phenomena in many branches of science within the context of Information Theory and Thermodynamics. They are typically approached by a sequence of independent events or by a memoryless…
We investigate the ferromagnetic Ising model on the Erd\H{o}s-R\'enyi random graph $\mathbb{G}(n,m)$ with bounded average degree $d=2m/n$. Specifically, we determine the limiting distribution of $\log Z_{\mathbb{G}(n,m)}(\beta,B)$, where…
We demonstrate that there is an intimate relationship between the magnetic properties of Derrida's random energy model (REM) of spin glasses and the problem of joint source--channel coding in Information Theory. In particular, typical…