Condensation of fluctuations in and out of equilibrium

Abstract

Condensation of fluctuations is an interesting phenomenon conceptually distinct from condensation on average. One stricking feature is that, contrary to what happens on average, condensation of fluctuations may occurr even in the absence of interaction. The explanation emerges from the duality between large deviation events in the given system and typical events in a new and appropriately biased system. This surprising phenomenon is investigated in the context of the Gaussian model, chosen as paradigmatical non interacting system, before and after an istantaneous temperature quench. It is shown that the bias induces a mean-field-like effective interaction responsible of the condensation on average. Phase diagrams, covering both the equilibrium and the off-equilibrium regimes, are derived for observables representative of generic behaviors.

Dynamics of fluctuations in the Gaussian model with conserved dynamics

“…Note that, since smaller values of I correspond to a larger probability of the corresponding fluctuations, this signals that out of equilibrium, the chances for the system to reach a configuration affected by condensation increase, as already pointed out in Ref. [22].…”

“…where ϕ k (t) = V d xϕ( x, t)e i k· x are the Fourier components of the order parameter field (and similarly ζ k (t) for the noise η( x, t)), and ω k := k 2 + r. The field correlator reads [22]…”

Heat fluctuations of Brownian oscillators in nonstationary processes: Fluctuation theorem and condensation transition

“…As it is usually the case for large systems, fluctuations of extensive quantities, such as heat, obey a large deviation principle [24,25]. The non trivial feature, unexpected for a linear system, is that in the large deviation function there appears a singularity corresponding to a condensation transition [26][27][28]. This means, as briefly anticipated in the Introduction, that there exists a critical threshold Q c of the exchanged heat, such that fluctuations above threshold are due to a single oscillator.…”

“…This kind of problem was considered previously in Refs. [26][27][28], showing that fluctuations undergo a condensation transition. Briefly, by this is meant that fluctuations in a multi-component system do condense if there exists a critical threshold above which the fluctuation is feeded by just one of the components (or degrees of freedom).…”

Phase transitions in atypical systems induced by a condensation transition on graphs

“…The formation of such condensed configurations has been coined condensation of degrees. These are large de-viation events triggered by atypical fluctuations in the graph structure, similar to other random systems that exhibit condensation transitions driven by rare fluctuations [31,32].…”