72 research outputs found
Feedback cooling, measurement errors, and entropy production
The efficiency of a feedback mechanism depends on the precision of the
measurement outcomes obtained from the controlled system. Accordingly,
measurement errors affect the entropy production in the system. We explore this
issue in the context of active feedback cooling by modeling a typical cold
damping setup as a harmonic oscillator in contact with a heat reservoir and
submitted to a velocity-dependent feedback force that reduces the random
motion. We consider two models that distinguish whether the sensor continuously
measures the position of the resonator or directly its velocity (in practice,
an electric current). Adopting the standpoint of the controlled system, we
identify the `entropy pumping' contribution that describes the entropy
reduction due to the feedback control and that modifies the second law of
thermodynamics. We also assign a relaxation dynamics to the feedback mechanism
and compare the apparent entropy production in the system and the heat bath to
the total entropy production in the super-system that includes the controller.
In this context, entropy pumping reflects the existence of hidden degrees of
freedom and the apparent entropy production satisfies fluctuation theorems
associated to an effective Langevin dynamics.Comment: 27 pages, 3 figures. Added references and foonotes. Revised
discussion at the end of section 4. Results unchanged. To appear in J. Stat.
Mec
Comment on Thermodynamic uncertainty relation for time-delayed Langevin systems
An extension of the thermodynamic uncertainty relation (TUR) to time-delayed
Langevin systems has been recently proposed by T. V. Vu and Y. Hasegawa
(arXiv:1809.06610v2). Here we show that the derivation is erroneous.Comment: 2 pages, 1 figur
Stochastic dynamics of N bistable elements with global time-delayed interactions: towards an exact solution of the master equations for finite N
We consider a network of N noisy bistable elements with global time-delayed
couplings. In a two-state description, where elements are represented by Ising
spins, the collective dynamics is described by an infinite hierarchy of coupled
master equations which was solved at the mean-field level in the thermodynamic
limit. For a finite number of elements, an analytical description was deemed so
far intractable and numerical studies seemed to be necessary. In this paper we
consider the case of two interacting elements and show that a partial
analytical description of the stationary state is possible if the stochastic
process is time-symmetric. This requires some relationship between the
transition rates to be satisfied.Comment: 17 pages, 7 figure
A self-consistent Ornstein-Zernike approximation for the Random Field Ising model
We extend the self-consistent Ornstein-Zernike approximation (SCOZA), first
formulated in the context of liquid-state theory, to the study of the random
field Ising model. Within the replica formalism, we treat the quenched random
field as an annealed spin variable, thereby avoiding the usual average over the
random field distribution. This allows to study the influence of the
distribution on the phase diagram in finite dimensions. The thermodynamics and
the correlation functions are obtained as solutions of a set a coupled partial
differential equations with magnetization, temperature and disorder strength as
independent variables. A preliminary analysis based on high-temperature and 1/d
series expansions shows that the theory can predict accurately the dependence
of the critical temperature on disorder strength for dimensions d>4. For the
bimodal distribution, we find a tricritical point which moves to weaker fields
as the dimension is reduced. For the Gaussian distribution, a tricritical point
may appear for d slightly above 4.Comment: 29 pages, Revtex file, 2 figures included, submitted to `Phys. Rev.
B
The ferromagnetic q-state Potts model on three-dimensional lattices: a study for real values of q
We study the phase diagram of the ferromagnetic -state Potts model on the
various three-dimensional lattices for integer and non-integer values of .
Our approach is based on a thermodynamically self-consistent Ornstein-Zernike
approximation for the two-point correlation functions. We calculate the
transition temperatures and, when the transition is first order, the jump
discontinuities in the magnetization and the internal energy, as well as the
coordinates of the critical endpoint in external field. Our predictions are in
very good agreement with best available estimates. From the numerical study of
the region of weak first-order transition, we estimate the critical value
for which the transition changes from second to first-order. The limit
that describes the bond-percolation problem is also investigated.Comment: 25 pages,3 tables,8 figure
A self-consistent Ornstein-Zernike approximation for the Edwards-Anderson spin glass model
We propose a self-consistent Ornstein-Zernike approximation for studying the
Edwards-Anderson spin glass model. By performing two Legendre transforms in
replica space, we introduce a Gibbs free energy depending on both the
magnetizations and the overlap order parameters. The correlation functions and
the thermodynamics are then obtained from the solution of a set of coupled
partial differential equations. The approximation becomes exact in the limit of
infinite dimension and it provides a potential route for studying the stability
of the high-temperature phase against replica-symmetry breaking fluctuations in
finite dimensions. As a first step, we present the numerical predictions for
the freezing temperature and the zero-field thermodynamic properties above
freezing as a function of dimensionality.Comment: 19 pages, 1 figure. submitted to J. Stat. Phy
Numerical study of metastable states in the T=0 RFIM
We study numerically the number of single-spin-flip stable states in the T=0
Random Field Ising Model (RFIM) on random regular graphs of connectivity
and and on the cubic lattice. The annealed and quenched complexities
(i.e. the entropy densities) of the metastable states with given magnetization
are calculated as a function of the external magnetic field. The results show
that the appearance of a (disorder-induced) out-of-equilibrium phase transition
in the magnetization hysteresis loop at low disorder can be ascribed to a
change in the distribution of the metastable states in the field-magnetization
plane.Comment: 15 pages, 19 figure
Information thermodynamics for interacting stochastic systems without bipartite structure
Fluctuations in biochemical networks, e.g., in a living cell, have a complex
origin that precludes a description of such systems in terms of bipartite or
multipartite processes, as is usually done in the framework of stochastic
and/or information thermodynamics. This means that fluctuations in each
subsystem are not independent: subsystems jump simultaneously if the dynamics
is modeled as a Markov jump process, or noises are correlated for diffusion
processes. In this paper, we consider information and thermodynamic exchanges
between a pair of coupled systems that do not satisfy the bipartite property.
The generalization of information-theoretic measures, such as learning rates
and transfer entropy rates, to this situation is non-trivial and also involves
introducing several additional rates. We describe how this can be achieved in
the framework of general continuous-time Markov processes, without restricting
the study to the steady-state regime. We illustrate our general formalism on
the case of diffusion processes and derive an extension of the second law of
information thermodynamics in which the difference of transfer entropy rates in
the forward and backward time directions replaces the learning rate. As a side
result, we also generalize an important relation linking information theory and
estimation theory. To further obtain analytical expressions we treat in detail
the case of Ornstein-Uhlenbeck processes, and discuss the ability of the
various information measures to detect a directional coupling in the presence
of correlated noises. Finally, we apply our formalism to the analysis of the
directional influence between cellular processes in a concrete example, which
also requires considering the case of a non-bipartite and non-Markovian
process.Comment: 39 pages, 5 figures. Final version, to appear in J. Stat.Mec
The T=0 RFIM on a Bethe lattice: correlation functions along the hysteresis loop
We consider the Gaussian random field Ising model (RFIM) on the Bethe lattice
at zero temperature in the presence of a uniform external field and derive the
exact expressions of the two-point spin-spin and spin-random field correlation
functions along the saturation hysteresis loop. To complete the analytical
description and suggest possible approximations for the RFIM on Euclidian
lattices we also compute the corresponding direct correlation functions (or
proper vertices) and show that they decay rapidly with the distance in the
weak-coupling/large disorder regime; their range, however, is not limited to
the nearest-neighbor distance.Comment: 13 pages, 7 figure
Spontaneous imbibition in disordered porous solids: a theoretical study of helium in silica aerogels
We present a theoretical study of spontaneous imbibition of liquid 4He in
silica aerogels focusing on the effect of porosity on the fluid dynamical
behavior. We adopt a coarse-grained three-dimensional lattice-gas description
like in previous studies of gas adsorption and capillary condensation, and use
a dynamical mean-field theory, assuming that capillary disorder predominates
over permeability disorder as in recent phase-field models of spontaneous
imbibition. Our results reveal a remarkable connection between imbibition and
adsorption as also suggested by recent experiments. The imbibition front is
always preceded by a precursor film and the classical Lucas-Washburn scaling
law is generally recovered, although some deviations may exist at large
porosity. Moreover, the interface roughening is modified by wetting and
confinement effects. Our results suggest that the interpretation of the recent
experiments should be revised.Comment: 13 pages, 16 figure
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