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The emergence of global order in complex systems with locally interacting components is most striking at criticality, where small changes in control parameters result in a sudden global re-organization. We introduce a measure of…
The thermal and statistical properties of hadronic matter under some extreme conditions are investigated using an exactly solvable canonical ensemble model. A unified model describing both the fragmentation of nuclei and the thermal…
We provide a probabilistic analysis of the banker algorithm when transition probabilities may depend on time and space. The transition probabilities evolve, as time goes by, along the trajectory of an ergodic Markovian environment, whereas…
We argue that the freezing transition scenario, previously explored in the statistical mechanics of 1/f-noise random energy models, also determines the value distribution of the maximum of the modulus of the characteristic polynomials of…
The established thermodynamic formalism of chaotic dynamics, valid at statistical equilibrium, is here generalized to systems out of equilibrium, that have yet to relax to a steady state. A relation between information, escape rate, and the…
Here we present a combinatorial decision problem, inspired by the celebrated quiz show called the countdown, that involves the computation of a given target number T from a set of k randomly chosen integers along with a set of arithmetic…
Temporal evolutions toward thermal equilibria are numerically investigated in a Hamiltonian system with many degrees of freedom which has second order phase transition. Relaxation processes are studied through local order parameter, and…
The field of quantum simulations in ultra-cold atomic gases has been remarkably successful. In principle it allows for an exact treatment of a variety of highly relevant lattice models and their emergent phases of matter. But so far there…
In the realm of statistical mechanics, it has been established that there is no distinction between the micro-canonical and canonical ensembles in the thermodynamic limit. However, this paradigm may alter when addressing statistical…
Recent results concerning the topological properties of random geometrical sets have been successfully applied to the study of the morphology of clusters in percolation theory. This approach provides an alternative way of inspecting the…
We consider a variant of the randomly reinforced urn where more balls can be simultaneously drawn out and balls of different colors can be simultaneously added. More precisely, at each time-step, the conditional distribution of the number…
Phase transitions in nuclei, small atomic clusters and self-gravitating systems demand the extension of thermo-statistics to ``Small'' systems. The main obstacle is the thermodynamic limit. It is shown how the original definition of the…
In a physical system, changing parameters such as temperature can induce a phase transition: an abrupt change from one state of matter to another. Analogous phenomena have recently been observed in large language models. Typically, the task…
The generalized P\`olya urn (GPU) models and their variants have been investigated in several disciplines. However, typical assumptions made with respect to the GPU do not include urn models with diagonal replacement matrix, which arise in…
We investigate the impact of the finite volume and the thermal fluctuations on the Critical End Point of the QCD phase diagram. To do so, we implement the super statistics framework with Gamma, $F$, and log-normal distributions and their…
Standard statistical mechanical or condensed matter arguments tell us that bulk properties of a physical system do not depend too much on boundary conditions. Random tilings of large regions provide counterexamples to such intuition, as…
We examine the minimization of information entropy for measures on the phase space of bounded domains, subject to constraints that are averages of grand canonical distributions. We describe the set of all such constraints and show that it…
The role of thermodynamics in the evolution of systems evolving under purely gravitational forces is not completely established. Both the infinite range and singularity in the Newtonian force law preclude the use of standard techniques.…
We review selected advances in the theoretical understanding of complex quantum many-body systems with regard to emergent notions of quantum statistical mechanics. We cover topics such as equilibration and thermalisation in pure state…
We propose an iterative proposal to estimate critical points for statistical models based on configurations by combing machine-learning tools. Firstly, phase scenarios and preliminary boundaries of phases are obtained by…