The nonequilibrium short-time critical behaviors of driven and undriven lattice gases are investigated via Monte Carlo simulations in two spatial dimensions starting from a fully disordered initial configuration. In particular, we study the time evolution of suitably defined order parameters, which account for the strong anisotropy introduced by the homogeneous drive. We demonstrate that, at short times, the dynamics of all these models is unexpectedly described by an effective continuum theory in which transverse fluctuations, i.e., fluctuations averaged along the drive, are Gaussian, irrespective of this being actually the case in the stationary state. Strong numerical evidence is provided, in remarkable agreement with that theory, both for the driven and undriven lattice gases, which therefore turn out to display the same short-time dynamics. Understanding the emergence of collective behaviours in statistical systems out of equilibrium is one of the major challenges of modern physics. Within a bottom-up approach, simplified lattice models were proposed in the past in order to capture specific aspects of nonequilibrium physics, e.g., the presence of external forces which induce steady currents in a system. The driven lattice gas (DLG) is perhaps the simplest among them: it generalizes the equilibrium lattice gas (LG) [1] to account for the presence of an external driving field E which acts along one lattice direction, biasing the particle jump rates. The DLG was introduced in 1983 [2] and it has since become the paradigm for driven diffusive systems [3,4]. At half filling, for any value of E, its stationary state shows a nonequilibrium continuous transition from a disordered to an ordered state at a critical temperature T c (E). In the ordered "phase" particles and holes are separated by an interface parallel to the direction of E [2-4]. The drive introduces also a strong spatial anisotropy and the observed transition differs from that of the Ising universality class (E = 0).In spite of the apparent simplicity of the model, the critical behaviour of the DLG has been a matter of debate for the past three decades. Early field-theoretical studies [5] proposed that the evolution of DLG is effectively described by a mesoscopic Langevin equation with spatial anisotropy and a finite particle current near the critical point. Within this theory (referred to as JSLC, from the authors' names), the critical behaviour of the transverse fluctuations turn out to arXiv:1607.01689v2 [cond-mat.stat-mech]

Using public data (Forbes Global 2000) we show that the asset sizes for the largest global firms follow a Pareto distribution in an intermediate range, that is “interrupted” by a sharp cut-off in its upper tail, where it is totally dominated by financial firms. This flattening of the distribution contrasts with a large body of empirical literature which finds a Pareto distribution for firm sizes both across countries and over time. Pareto distributions are generally traced back to a mechanism of proportional random growth, based on a regime of constant returns to scale. This makes our findings of an “interrupted” Pareto distribution all the more puzzling, because we provide evidence that financial firms in our sample should operate in such a regime. We claim that the missing mass from the upper tail of the asset size distribution is a consequence of shadow banking activity and that it provides an (upper) estimate of the size of the shadow banking system. This estimate–which we propose as a shadow banking index–compares well with estimates of the Financial Stability Board until 2009, but it shows a sharper rise in shadow banking activity after 2010. Finally, we propose a proportional random growth model that reproduces the observed distribution, thereby providing a quantitative estimate of the intensity of shadow banking activity.

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The dynamic and static critical behaviors of driven and equilibrium lattice gas models are studied in two spatial dimensions. We show that in the short-time regime immediately following a critical quench, the dynamics of the transverse anisotropic order parameter, its autocorrelation, and Binder cumulant are consistent with the prediction of a Gaussian, i.e., noninteracting, effective theory, both for the nonequilibrium lattice gases and, to some extent, their equilibrium counterpart. Such a superuniversal behavior is observed only at short times after a critical quench, while the various models display their distinct behaviors in the stationary states, described by the corresponding, known universality classes.