3,297 research outputs found
On the work distribution for the adiabatic compression of a dilute classical gas
We consider the adiabatic and quasi-static compression of a dilute classical
gas, confined in a piston and initially equilibrated with a heat bath. We find
that the work performed during this process is described statistically by a
gamma distribution. We use this result to show that the model satisfies the
non-equilibrium work and fluctuation theorems, but not the
flucutation-dissipation relation. We discuss the rare but dominant realizations
that contribute most to the exponential average of the work, and relate our
results to potentially universal work distributions.Comment: 4 page
Neural Relax
We present an algorithm for data preprocessing of an associative memory
inspired to an electrostatic problem that turns out to have intimate relations
with information maximization
Domain wall propagation and nucleation in a metastable two-level system
We present a dynamical description and analysis of non-equilibrium
transitions in the noisy one-dimensional Ginzburg-Landau equation for an
extensive system based on a weak noise canonical phase space formulation of the
Freidlin-Wentzel or Martin-Siggia-Rose methods. We derive propagating nonlinear
domain wall or soliton solutions of the resulting canonical field equations
with superimposed diffusive modes. The transition pathways are characterized by
the nucleations and subsequent propagation of domain walls. We discuss the
general switching scenario in terms of a dilute gas of propagating domain walls
and evaluate the Arrhenius factor in terms of the associated action. We find
excellent agreement with recent numerical optimization studies.Comment: 28 pages, 16 figures, revtex styl
Synchronization and Redundancy: Implications for Robustness of Neural Learning and Decision Making
Learning and decision making in the brain are key processes critical to
survival, and yet are processes implemented by non-ideal biological building
blocks which can impose significant error. We explore quantitatively how the
brain might cope with this inherent source of error by taking advantage of two
ubiquitous mechanisms, redundancy and synchronization. In particular we
consider a neural process whose goal is to learn a decision function by
implementing a nonlinear gradient dynamics. The dynamics, however, are assumed
to be corrupted by perturbations modeling the error which might be incurred due
to limitations of the biology, intrinsic neuronal noise, and imperfect
measurements. We show that error, and the associated uncertainty surrounding a
learned solution, can be controlled in large part by trading off
synchronization strength among multiple redundant neural systems against the
noise amplitude. The impact of the coupling between such redundant systems is
quantified by the spectrum of the network Laplacian, and we discuss the role of
network topology in synchronization and in reducing the effect of noise. A
range of situations in which the mechanisms we model arise in brain science are
discussed, and we draw attention to experimental evidence suggesting that
cortical circuits capable of implementing the computations of interest here can
be found on several scales. Finally, simulations comparing theoretical bounds
to the relevant empirical quantities show that the theoretical estimates we
derive can be tight.Comment: Preprint, accepted for publication in Neural Computatio
On the Stability of the Mean-Field Glass Broken Phase under Non-Hamiltonian Perturbations
We study the dynamics of the SK model modified by a small non-hamiltonian
perturbation. We study aging, and we find that on the time scales investigated
by our numerical simulations it survives a small perturbation (and is destroyed
by a large one). If we assume we are observing a transient behavior the scaling
of correlation times versus the asymmetry strength is not compatible with the
one expected for the spherical model. We discuss the slow power law decay of
observable quantities to equilibrium, and we show that for small perturbations
power like decay is preserved. We also discuss the asymptotically large time
region on small lattices.Comment: 34 page
The Measure-theoretic Identity Underlying Transient Fluctuation Theorems
We prove a measure-theoretic identity that underlies all transient
fluctuation theorems (TFTs) for entropy production and dissipated work in
inhomogeneous deterministic and stochastic processes, including those of Evans
and Searles, Crooks, and Seifert. The identity is used to deduce a tautological
physical interpretation of TFTs in terms of the arrow of time, and its
generality reveals that the self-inverse nature of the various trajectory and
process transformations historically relied upon to prove TFTs, while necessary
for these theorems from a physical standpoint, is not necessary from a
mathematical one. The moment generating functions of thermodynamic variables
appearing in the identity are shown to converge in general only in a vertical
strip in the complex plane, with the consequence that a TFT that holds over
arbitrary timescales may fail to give rise to an asymptotic fluctuation theorem
for any possible speed of the corresponding large deviation principle. The case
of strongly biased birth-death chains is presented to illustrate this
phenomenon. We also discuss insights obtained from our measure-theoretic
formalism into the results of Saha et. al. on the breakdown of TFTs for driven
Brownian particles
Stochastic learning in a neural network with adapting synapses
We consider a neural network with adapting synapses whose dynamics can be
analitically computed. The model is made of neurons and each of them is
connected to input neurons chosen at random in the network. The synapses
are -states variables which evolve in time according to Stochastic Learning
rules; a parallel stochastic dynamics is assumed for neurons. Since the network
maintains the same dynamics whether it is engaged in computation or in learning
new memories, a very low probability of synaptic transitions is assumed. In the
limit with large and finite, the correlations of neurons and
synapses can be neglected and the dynamics can be analitically calculated by
flow equations for the macroscopic parameters of the system.Comment: 25 pages, LaTeX fil
Microcanonical quantum fluctuation theorems
Previously derived expressions for the characteristic function of work
performed on a quantum system by a classical external force are generalized to
arbitrary initial states of the considered system and to Hamiltonians with
degenerate spectra. In the particular case of microcanonical initial states
explicit expressions for the characteristic function and the corresponding
probability density of work are formulated. Their classical limit as well as
their relations to the respective canonical expressions are discussed. A
fluctuation theorem is derived that expresses the ratio of probabilities of
work for a process and its time reversal to the ratio of densities of states of
the microcanonical equilibrium systems with corresponding initial and final
Hamiltonians.From this Crooks-type fluctuation theorem a relation between
entropies of different systems can be derived which does not involve the time
reversed process. This entropy-from-work theorem provides an experimentally
accessible way to measure entropies.Comment: revised and extended versio
Effective Critical Exponents for Dimensional Ccrossover and Quantum Systems from an Environmentally Friendly Renormalization Group
Series for the Wilson functions of an ``environmentally friendly''
renormalization group are computed to two loops, for an vector model, in
terms of the ``floating coupling'', and resummed by the Pad\'e method to yield
crossover exponents for finite size and quantum systems. The resulting
effective exponents obey all scaling laws, including hyperscaling in terms of
an effective dimensionality, {d\ef}=4-\gl, which represents the crossover in
the leading irrelevant operator, and are in excellent agreement with known
results.Comment: 10 pages of Plain Tex, Postscript figures available upon request from
[email protected], preprint numbers THU-93/18, DIAS-STP-93-1
Dynamic scaling regimes of collective decision making
We investigate a social system of agents faced with a binary choice. We
assume there is a correct, or beneficial, outcome of this choice. Furthermore,
we assume agents are influenced by others in making their decision, and that
the agents can obtain information that may guide them towards making a correct
decision. The dynamic model we propose is of nonequilibrium type, converging to
a final decision. We run it on random graphs and scale-free networks. On random
graphs, we find two distinct regions in terms of the "finalizing time" -- the
time until all agents have finalized their decisions. On scale-free networks on
the other hand, there does not seem to be any such distinct scaling regions
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