Statistical Mechanics
Geometry of bounded critical phenomena (1904.08919v1)
Giacomo Gori, Andrea Trombettoni
2019-04-18
We devise a geometric description of bounded systems at criticality in any dimension
. This is achieved by altering the flat metric with a space dependent scale factor
,
belonging to a general bounded domain
.
. For the 3D Ising model we find
which favorably compares (at the fifth decimal place) with the state-of-the-art estimate. A nontrivial prediction is the structure of two-point correlators at criticality. They should depend on the fractional Q-hyperbolic distance calculated from the metric, in turn depending only on the shape of the bounded domain and on
Thermodynamics of Chemical Waves (1904.08874v1)
Francesco Avanzini, Gianmaria Falasco, Massimiliano Esposito
2019-04-18
Chemical waves constitute a known class of dissipative structures emerging in reaction-diffusion systems. They play a crucial role in biology, spreading information rapidly to synchronize and coordinate biological events. We develop a rigorous thermodynamic theory of reaction-diffusion systems to characterize chemical waves. Our main result is the definition of the proper thermodynamic potential of the local dynamics as a nonequilibrium free energy density and establishing its balance equation. This enables us to identify the dynamics of the free energy, of the dissipation, and of the work spent to sustain the wave propagation. Two prototypical classes of chemical waves are examined. From a thermodynamic perspective, the first is sustained by relaxation towards equilibrium and the second by nonconservative forces generated by chemostats. We analytically study step-like waves, called wavefronts, using the Fisher-Kolmogorov equation as representative of the first class and oscillating waves in the Brusselator model as representative of the second. Given the fundamental role of chemical waves as message carriers in biosystems, our thermodynamic theory constitutes an important step toward an understanding of information transfers and processing in biology.
Two localization lengths in the Anderson transition on random graphs (1904.08869v1)
I. García-Mata, J. Martin, R. Dubertrand, O. Giraud, B. Georgeot, G. Lemarié
2019-04-18
We present a full description of the nonergodic properties of wavefunctions on random graphs without boundary in the localized and critical regimes of the Anderson transition. We find that they are characterized by two localization lengths: the largest one describes localization along rare branches and diverges at the transition, while the second one describes localization along typical branches and remains finite at criticality. We show numerically that both quantities can be extracted from several different physical quantities: wavefunction moments, correlation functions and spectral statistics. These different localization lengths are associated with two different critical exponents, which control the finite-size scaling properties of the system close to the transition. Our approach could be directly applied to the many-body localization transition and more generally to nonergodic properties of states in Hilbert space.
Algorithmic complexity of multiplex networks (1903.08049v2)
A. Santoro, V. Nicosia
2019-03-19
Multilayer networks preserve full information about the different interactions among the constituents of a complex system, and have recently proven quite useful in modelling transportation networks, social circles, and the human brain. A fundamental and still open problem is to assess if and when the multilayer representation of a system is a qualitatively better model than the classical single-layer aggregated network approach. Here we tackle this problem from an algorithmic information theory perspective. We propose an intuitive way to encode a multilayer network into a bit string, and we define the complexity of a multilayer network as the ratio of the Kolmogorov complexity of the bit strings associated to the multilayer and to the corresponding aggregated graph. We find that there exists a maximum amount of additional information that a multilayer model can encode with respect to an equivalent single-layer graph. We show how our measure can be used to obtain low-dimensional representations of multidimensional systems, to cluster multilayer networks into a small set of meaningful super-families, and to detect tipping points in different time-varying multilayer graphs. These results suggest that information-theoretic approaches can be effectively employed in the study of multi-dimensional complex systems, and pave the way to a more systematic analysis of static and time-varying multidimensional complex systems.
Quantum to classical transition in an information ratchet (1808.02802v2)
Josey Stevens, Sebastian Deffner
2018-08-08
Recent years have seen a flurry of research activity in the study of minimal and autonomous information ratchets. However, the existing classical and quantum models are somewhat hard to compare, and, hence, quantifying possible quantum supremacy in information ratchets has been elusive. We propose a first step towards filling this void between quantum and classical ratchets by introducing a new model with continuous variables -- a quantum particle in a box coupled to a stream of qubits. The dynamics is solved exactly, and we analyze the quantum to classical transition in terms of a natural time scale parameter for the model.
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