10,968 research outputs found
On time-reversibility of linear stochastic models
Reversal of the time direction in stochastic systems driven by white noise
has been central throughout the development of stochastic realization theory,
filtering and smoothing. Similar ideas were developed in connection with
certain problems in the theory of moments, where a duality induced by time
reversal was introduced to parametrize solutions. In this latter work it was
shown that stochastic systems driven by arbitrary second-order stationary
processes can be similarly time-reversed. By combining these two sets of ideas
we present herein a generalization of time-reversal in stochastic realization
theory.Comment: 10 pages, 4 figure
Reversibility and Non-reversibility in Stochastic Chemical Kinetics
Mathematical problems with mean field and local type interaction related to
stochastic chemical kinetics,are considered. Our main concern various
definitions of reversibility, their corollaries (Boltzmann type equations,
fluctuations, Onsager relations, etc.) and emergence of irreversibility
Linear and nonlinear time series analysis of the black hole candidate Cygnus X-1
We analyze the variability in the X-ray lightcurves of the black hole
candidate Cygnus X-1 by linear and nonlinear time series analysis methods.
While a linear model describes the over-all second order properties of the
observed data well, surrogate data analysis reveals a significant deviation
from linearity. We discuss the relation between shot noise models usually
applied to analyze these data and linear stochastic autoregressive models. We
debate statistical and interpretational issues of surrogate data testing for
the present context. Finally, we suggest a combination of tools from linear
andnonlinear time series analysis methods as a procedure to test the
predictions of astrophysical models on observed data.Comment: 15 pages, to appear in Phys. Rev.
Errors, Correlations and Fidelity for noisy Hamilton flows. Theory and numerical examples
We analyse the asymptotic growth of the error for Hamiltonian flows due to
small random perturbations. We compare the forward error with the reversibility
error, showing their equivalence for linear flows on a compact phase space. The
forward error, given by the root mean square deviation of the noisy
flow, grows according to a power law if the system is integrable and according
to an exponential law if it is chaotic.
The autocorrelation and the fidelity, defined as the correlation of the
perturbed flow with respect to the unperturbed one, exhibit an exponential
decay as . Some numerical examples such as the
anharmonic oscillator and the H\'enon Heiles model confirm these results. We
finally consider the effect of the observational noise on an integrable system,
and show that the decay of correlations can only be observed after a sequence
of measurements and that the multiplicative noise is more effective if the
delay between two measurements is large.Comment: 22 pages, 3 figure
Equations for Stochastic Macromolecular Mechanics of Single Proteins: Equilibrium Fluctuations, Transient Kinetics and Nonequilibrium Steady-State
A modeling framework for the internal conformational dynamics and external
mechanical movement of single biological macromolecules in aqueous solution at
constant temperature is developed. Both the internal dynamics and external
movement are stochastic; the former is represented by a master equation for a
set of discrete states, and the latter is described by a continuous
Smoluchowski equation. Combining these two equations into one, a comprehensive
theory for the Brownian dynamics and statistical thermodynamics of single
macromolecules arises. This approach is shown to have wide applications. It is
applied to protein-ligand dissociation under external force, unfolding of
polyglobular proteins under extension, movement along linear tracks of motor
proteins against load, and enzyme catalysis by single fluctuating proteins. As
a generalization of the classic polymer theory, the dynamic equation is capable
of characterizing a single macromolecule in aqueous solution, in probabilistic
terms, (1) its thermodynamic equilibrium with fluctuations, (2) transient
relaxation kinetics, and most importantly and novel (3) nonequilibrium
steady-state with heat dissipation. A reversibility condition which guarantees
an equilibrium solution and its thermodynamic stability is established, an
H-theorem like inequality for irreversibility is obtained, and a rule for
thermodynamic consistency in chemically pumped nonequilibrium steady-state is
given.Comment: 23 pages, 4 figure
Reversibility, heat dissipation and the importance of the thermal environment in stochastic models of nonequilibrium steady states
We examine stochastic processes that are used to model nonequilibrium
processes (e.g, pulling RNA or dragging colloids) and so deliberately violate
detailed balance. We argue that by combining an information-theoretic measure
of irreversibility with nonequilibrium work theorems, the thermal physics
implied by abstract dynamics can be determined. This measure is bounded above
by thermodynamic entropy production and so may quantify how well a stochastic
dynamics models reality. We also use our findings to critique various modeling
approaches and notions arising in steady-state thermodynamics.Comment: 8 pages, 2 figures, easy-to-read, single-column, large-print RevTeX4
format; version with modified abstract and additional discussion, references
to appear in Phys Rev Let
Fluctuations in Nonequilibrium Statistical Mechanics: Models, Mathematical Theory, Physical Mechanisms
The fluctuations in nonequilibrium systems are under intense theoretical and
experimental investigation. Topical ``fluctuation relations'' describe
symmetries of the statistical properties of certain observables, in a variety
of models and phenomena. They have been derived in deterministic and, later, in
stochastic frameworks. Other results first obtained for stochastic processes,
and later considered in deterministic dynamics, describe the temporal evolution
of fluctuations. The field has grown beyond expectation: research works and
different perspectives are proposed at an ever faster pace. Indeed,
understanding fluctuations is important for the emerging theory of
nonequilibrium phenomena, as well as for applications, such as those of
nanotechnological and biophysical interest. However, the links among the
different approaches and the limitations of these approaches are not fully
understood. We focus on these issues, providing: a) analysis of the theoretical
models; b) discussion of the rigorous mathematical results; c) identification
of the physical mechanisms underlying the validity of the theoretical
predictions, for a wide range of phenomena.Comment: 44 pages, 2 figures. To appear in Nonlinearity (2007
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