4,486 research outputs found
A statistical physics perspective on criticality in financial markets
Stock markets are complex systems exhibiting collective phenomena and
particular features such as synchronization, fluctuations distributed as
power-laws, non-random structures and similarity to neural networks. Such
specific properties suggest that markets operate at a very special point.
Financial markets are believed to be critical by analogy to physical systems
but few statistically founded evidence have been given. Through a data-based
methodology and comparison to simulations inspired by statistical physics of
complex systems, we show that the Dow Jones and indices sets are not rigorously
critical. However, financial systems are closer to the criticality in the crash
neighborhood.Comment: 23 pages, 19 figure
Hamiltonian Dynamics of Yang-Mills Fields on a Lattice
We review recent results from studies of the dynamics of classical Yang-Mills
fields on a lattice. We discuss the numerical techniques employed in solving
the classical lattice Yang-Mills equations in real time, and present results
exhibiting the universal chaotic behavior of nonabelian gauge theories. The
complete spectrum of Lyapunov exponents is determined for the gauge group
SU(2). We survey results obtained for the SU(3) gauge theory and other
nonlinear field theories. We also discuss the relevance of these results to the
problem of thermalization in gauge theories.Comment: REVTeX, 51 pages, 20 figure
Nonlocal probes of thermalization in holographic quenches with spectral methods
We describe the application of pseudo-spectral methods to problems of
holographic thermal quenches of relevant couplings in strongly coupled gauge
theories. We focus on quenches of a fermionic mass term in a strongly coupled
N=4 supersymmetric Yang-Mills plasma, and the subsequent equilibration of the
system. From the dual gravitational perspective, we study the gravitational
collapse of a massive scalar field in asymptotically anti-de Sitter geometry
with a prescribed boundary condition for its non-normalizable mode. Access to
the full background geometry of the gravitational collapse allows for the study
of nonlocal probes of the thermalization process. We discuss the evolution of
the apparent and the event horizons, the two-point correlation functions of
operators of large conformal dimensions, and the evolution of the entanglement
entropy of the system. We compare the thermalization process from the viewpoint
of local (the one-point) correlation functions and these nonlocal probes,
finding that the thermalization time as measured by the probes is length
dependent, and approaches the thermalization time of the one-point function for
longer probes. We further discuss how the different energy scales of the
problem contribute to its thermalization.Comment: 83 pages, 25 figures. v2: Corrected constraint in equation (A.26),
which led to non-monotonic apparent horizons in our simulations. Replaced
most figures. Added equation (4.11). Added references [37], [38]. Added
acknowledgement. Corrected some typos. Most conclusions remain unchange
Adaptation to criticality through organizational invariance in embodied agents
Many biological and cognitive systems do not operate deep within one or other
regime of activity. Instead, they are poised at critical points located at
phase transitions in their parameter space. The pervasiveness of criticality
suggests that there may be general principles inducing this behaviour, yet
there is no well-founded theory for understanding how criticality is generated
at a wide span of levels and contexts. In order to explore how criticality
might emerge from general adaptive mechanisms, we propose a simple learning
rule that maintains an internal organizational structure from a specific family
of systems at criticality. We implement the mechanism in artificial embodied
agents controlled by a neural network maintaining a correlation structure
randomly sampled from an Ising model at critical temperature. Agents are
evaluated in two classical reinforcement learning scenarios: the Mountain Car
and the Acrobot double pendulum. In both cases the neural controller appears to
reach a point of criticality, which coincides with a transition point between
two regimes of the agent's behaviour. These results suggest that adaptation to
criticality could be used as a general adaptive mechanism in some
circumstances, providing an alternative explanation for the pervasive presence
of criticality in biological and cognitive systems.Comment: arXiv admin note: substantial text overlap with arXiv:1704.0525
Extinction of metastable stochastic populations
We investigate extinction of a long-lived self-regulating stochastic
population, caused by intrinsic (demographic) noise. Extinction typically
occurs via one of two scenarios depending on whether the absorbing state n=0 is
a repelling (scenario A) or attracting (scenario B) point of the deterministic
rate equation. In scenario A the metastable stochastic population resides in
the vicinity of an attracting fixed point next to the repelling point n=0. In
scenario B there is an intermediate repelling point n=n_1 between the
attracting point n=0 and another attracting point n=n_2 in the vicinity of
which the metastable population resides. The crux of the theory is WKB method
which assumes that the typical population size in the metastable state is
large. Starting from the master equation, we calculate the quasi-stationary
probability distribution of the population sizes and the (exponentially long)
mean time to extinction for each of the two scenarios. When necessary, the WKB
approximation is complemented (i) by a recursive solution of the
quasi-stationary master equation at small n and (ii) by the van Kampen
system-size expansion, valid near the fixed points of the deterministic rate
equation. The theory yields both entropic barriers to extinction and
pre-exponential factors, and holds for a general set of multi-step processes
when detailed balance is broken. The results simplify considerably for
single-step processes and near the characteristic bifurcations of scenarios A
and B.Comment: 19 pages, 7 figure
Deriving GENERIC from a generalized fluctuation symmetry
Much of the structure of macroscopic evolution equations for relaxation to
equilibrium can be derived from symmetries in the dynamical fluctuations around
the most typical trajectory. For example, detailed balance as expressed in
terms of the Lagrangian for the path-space action leads to gradient zero-cost
flow. We find a new such fluctuation symmetry that implies GENERIC, an
extension of gradient flow where a Hamiltonian part is added to the dissipative
term in such a way as to retain the free energy as Lyapunov function
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