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Carrying out explicitly the computation in a paradigmatic model of non-interacting systems, the Gaussian Model, we show the existence of a singular point in the probability distribution $P(M)$ of an extensive variable $M$. Interpreting $P(M)$ as a thermodynamic potential of a dual system obtained from the original one by applying a constraint, we discuss how the non-analytical point of $P(M)$ is the counterpart of a phase-transition in the companion system. We show the generality of such mechanism by considering both the system in equilibrium or in the non-equilibrium state following a temperature quench.
We have exactly solved the relaxational dynamics of a model protein which possesses a kinetically perfect funnel-like energy landscape. We find that the dependence of the relaxation time, $tau$, on the density of states (DOS) and the energy level spa
The ``Brownian bees model describes an ensemble of $N$ independent branching Brownian particles. When a particle branches into two particles, the particle farthest from the origin is eliminated so as to keep a constant number of particles. In the lim
We predict the emergence of turbulent scaling in the quench dynamics of the two-dimensional Heisenberg model for a wide range of initial conditions and model parameters. In the isotropic Heisenberg model, we find that the spin-spin correlation functi
Fluctuations of energy and heat are investigated during the relaxation following the instantaneous temperature quench of an extended system. Results are obtained analytically for the Gaussian model and for the large $N$ model quenched below the criti
We study the relaxation process in a two-dimensional lattice gas model, where the interactions come from the excluded volume. In this model particles have three arms with an asymmetrical shape, which results in geometrical frustration that inhibits f