458 research outputs found
Entropy production for coarse-grained dynamics
Systems out of equilibrium exhibit a net production of entropy. We study the
dynamics of a stochastic system represented by a Master Equation that can be
modeled by a Fokker-Planck equation in a coarse-grained, mesoscopic
description. We show that the corresponding coarse-grained entropy production
contains information on microscopic currents that are not captured by the
Fokker-Planck equation and thus cannot be deduced from it. We study a
discrete-state and a continuous-state system, deriving in both the cases an
analytical expression for the coarse-graining corrections to the entropy
production. This result elucidates the limits in which there is no loss of
information in passing from a Master Equation to a Fokker-Planck equation
describing the same system. Our results are amenable of experimental
verification, which could help to infer some information about the underlying
microscopic processes
Entropy production in systems with unidirectional transitions
The entropy production is one of the most essential features for systems
operating out of equilibrium. The formulation for discrete-state systems goes
back to the celebrated Schnakenberg's work and hitherto can be carried out when
for each transition between two states also the reverse one is allowed.
Nevertheless, several physical systems may exhibit a mixture of both
unidirectional and bidirectional transitions, and how to properly define the
entropy production in this case is still an open question. Here, we present a
solution to such a challenging problem. The average entropy production can be
consistently defined, employing a mapping that preserves the average fluxes,
and its physical interpretation is provided. We describe a class of stochastic
systems composed of unidirectional links forming cycles and detailed-balanced
bidirectional links, showing that they behave in a pseudo-deterministic
fashion. This approach is applied to a system with time-dependent stochastic
resetting. Our framework is consistent with thermodynamics and leads to some
intriguing observations on the relation between the arrow of time and the
average entropy production for resetting events.Comment: (Accepted for publication in Physical Review Research
Quantum Critical Behavior of Disordered Superfluids
The quantum critical behavior of an interacting, non-relativistic Bose theory
with quenched disorder randomly distributed in space is investigated. The
renormalization group is carried out in a double expansion, where
one is the deviation of the effective space-time dimensionality from
4, while the other denotes the number of time dimensions. The disordered
theory, which displays localization in the superfluid state, is shown to
possess an infrared stable fixed point.Comment: REVTEX, 5 page
Dynamic nonlinear (cubic) susceptibility in quantum Ising spin glass
Dynamic nonlinear (cubic) susceptibility in quantum d-dimensional Ising spin
glass with short-range interactions is investigated on the basis of quantum
droplet model and quantum-mechanical nonlinear response theory. Nonlinear
response depends on the tunneling rate for a droplet which regulates the
strength of quantum fluctuations. It shows a strong dependence on the
distribution of droplet free energies and on the droplet length scale average.
Comparison with recent experiments on quantum spin glasses like disordered
dipolar quantum Ising magnet is discussed.Comment: 15 pages, 3 figure
Turing patterns in multiplex networks
The theory of patterns formation for a reaction-diffusion system defined on a
multiplex is developed by means of a perturbative approach. The intra-layer
diffusion constants act as small parameter in the expansion and the unperturbed
state coincides with the limiting setting where the multiplex layers are
decoupled. The interaction between adjacent layers can seed the instability of
an homogeneous fixed point, yielding self-organized patterns which are instead
impeded in the limit of decoupled layers. Patterns on individual layers can
also fade away due to cross-talking between layers. Analytical results are
compared to direct simulations
Pattern formation for reactive species undergoing anisotropic diffusion
Turing instabilities for a two species reaction-diffusion systems is studied
under anisotropic diffusion. More specifically, the diffusion constants which
characterize the ability of the species to relocate in space are direction
sensitive. Under this working hypothesis, the conditions for the onset of the
instability are mathematically derived and numerically validated. Patterns
which closely resemble those obtained in the classical context of isotropic
diffusion, develop when the usual Turing condition is violated, along one of
the two accessible directions of migration. Remarkably, the instability can
also set in when the activator diffuses faster than the inhibitor, along the
direction for which the usual Turing conditions are not matched
Hyperaccurate currents in stochastic thermodynamics
Thermodynamic observables of mesoscopic systems can be expressed as integrated empirical currents. Their fluctuations are bound by thermodynamic uncertainty relations. We introduce the hyperaccurate current as the integrated empirical current with the least fluctuations in a given nonequilibrium system. For steady-state systems described by overdamped Langevin equations, we derive an equation for the hyperaccurate current by means of a variational principle. We show that the hyperaccurate current coincides with the entropy production if and only if the latter saturates the thermodynamic uncertainty relation, and it can be substantially more precise otherwise. The hyperaccurate current can be used to improve estimates of entropy production from experimental data
Mutual information in changing environments: non-linear interactions, out-of-equilibrium systems, and continuously-varying diffusivities
Biochemistry, ecology, and neuroscience are examples of prominent fields
aiming at describing interacting systems that exhibit non-trivial couplings to
complex, ever-changing environments. We have recently shown that linear
interactions and a switching environment are encoded separately in the mutual
information of the overall system. Here, we first generalize these findings to
a broad class of non-linear interacting models. We find that a new term in the
mutual information appears, quantifying the interplay between non-linear
interactions and environmental changes, and leading to either constructive or
destructive information interference. Furthermore, we show that a higher mutual
information emerges in out-of-equilibrium environments with respect to an
equilibrium scenario. Finally, we generalize our framework to the case of
continuously varying environments. We find that environmental changes can be
mapped exactly into an effective spatially-varying diffusion coefficient,
shedding light on modeling and information structure of biophysical systems in
inhomogeneous media
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