1,735 research outputs found
Thermodynamic bounds on equilibrium fluctuations of a global or local order parameter
We analyze thermodynamic bounds on equilibrium fluctuations of an order
parameter, which are analogous to relations, which have been derived recently
in the context of non-equilibrium fluctuations of currents. We discuss the case
of {\it global} fluctuations when the order parameter is measured in the full
system of interest, and {\it local} fluctuations, when the order parameter is
evaluated only in a sub-part of the system. Using isometric fluctuation
theorems, we derive thermodynamic bounds on the fluctuations of the order
parameter in both cases. These bounds could be used to infer the value of
symmetry breaking field or the relative size of the observed sub-system to the
full system from {\it local} fluctuations.Comment: 8 pages, 6 figures, in press for Europhys. Let
A Poisson-Boltzmann approach for a lipid membrane in an electric field
The behavior of a non-conductive quasi-planar lipid membrane in an
electrolyte and in a static (DC) electric field is investigated theoretically
in the nonlinear (Poisson-Boltzmann) regime. Electrostatic effects due to
charges in the membrane lipids and in the double layers lead to corrections to
the membrane elastic moduli which are analyzed here. We show that, especially
in the low salt limit, i) the electrostatic contribution to the membrane's
surface tension due to the Debye layers crosses over from a quadratic behavior
in the externally applied voltage to a linear voltage regime. ii) the
contribution to the membrane's bending modulus due to the Debye layers
saturates for high voltages. Nevertheless, the membrane undulation instability
due to an effectively negative surface tension as predicted by linear
Debye-H\"uckel theory is shown to persist in the nonlinear, high voltage
regime.Comment: 15 pages, 4 figure
Phase transitions in optimal strategies for betting
Kelly's criterion is a betting strategy that maximizes the long term growth
rate, but which is known to be risky. Here, we find optimal betting strategies
that gives the highest capital growth rate while keeping a certain low value of
risky fluctuations. We then analyze the trade-off between the average and the
fluctuations of the growth rate, in models of horse races, first for two horses
then for an arbitrary number of horses, and for uncorrelated or correlated
races. We find an analog of a phase transition with a coexistence between two
optimal strategies, where one has risk and the other one does not. The above
trade-off is also embodied in a general bound on the average growth rate,
similar to thermodynamic uncertainty relations. We also prove mathematically
the absence of other phase transitions between Kelly's point and the risk free
strategy.Comment: 23 pages, 5 figure
Thermal expansion within a chain of magnetic colloidal particles
We study the thermal expansion of chains formed by self-assembly of magnetic
colloidal particles in a magnetic field. Using video-microscopy, complete
positional data of all the particles of the chains is obtained. By changing the
ionic strength of the solution and the applied magnetic field, the interaction
potential can be tuned. We analyze the thermal expansion of the chain using a
simple model of a one dimensional anharmonic crystal of finite size.Comment: 5 pages and 3 figure
The measurement of surface gravity
LaCoste and Romberg G and D gravity meters are normally employed when attempting high precision measurement of gravity differences on land. The capabilities and limitations of these instruments are discussed
Non-equilibrium fluctuations and mechanochemical couplings of a molecular motor
We investigate theoretically the violations of Einstein and Onsager
relations, and the efficiency for a single processive motor operating far from
equilibrium using an extension of the two-state model introduced by Kafri {\em
et al.} [Biophys. J. {\bf 86}, 3373 (2004)]. With the aid of the Fluctuation
Theorem, we analyze the general features of these violations and this
efficiency and link them to mechanochemical couplings of motors. In particular,
an analysis of the experimental data of kinesin using our framework leads to
interesting predictions that may serve as a guide for future experiments.Comment: 4 pages, 4 figures, accepted to Phys. Rev. Let
Information-theoretic analysis of the directional influence between cellular processes
Inferring the directionality of interactions between cellular processes is a
major challenge in systems biology. Time-lagged correlations allow to
discriminate between alternative models, but they still rely on assumed
underlying interactions. Here, we use the transfer entropy (TE), an
information-theoretic quantity that quantifies the directional influence
between fluctuating variables in a model-free way. We present a theoretical
approach to compute the transfer entropy, even when the noise has an extrinsic
component or in the presence of feedback. We re-analyze the experimental data
from Kiviet et al. (2014) where fluctuations in gene expression of metabolic
enzymes and growth rate have been measured in single cells of E. coli. We
confirm the formerly detected modes between growth and gene expression, while
prescribing more stringent conditions on the structure of noise sources. We
furthermore point out practical requirements in terms of length of time series
and sampling time which must be satisfied in order to infer optimally transfer
entropy from times series of fluctuations.Comment: 24 pages, 7 figure
Gallavotti-Cohen-Type symmetry related to cycle decompositions for Markov chains and biochemical applications
We slightly extend the fluctuation theorem obtained in \cite{LS} for sums of
generators, considering continuous-time Markov chains on a finite state space
whose underlying graph has multiple edges and no loop. This extended frame is
suited when analyzing chemical systems. As simple corollary we derive in a
different method the fluctuation theorem of D. Andrieux and P. Gaspard for the
fluxes along the chords associated to a fundamental set of oriented cycles
\cite{AG2}.
We associate to each random trajectory an oriented cycle on the graph and we
decompose it in terms of a basis of oriented cycles. We prove a fluctuation
theorem for the coefficients in this decomposition. The resulting fluctuation
theorem involves the cycle affinities, which in many real systems correspond to
the macroscopic forces. In addition, the above decomposition is useful when
analyzing the large deviations of additive functionals of the Markov chain. As
example of application, in a very general context we derive a fluctuation
relation for the mechanical and chemical currents of a molecular motor moving
along a periodic filament.Comment: 23 pages, 5 figures. Correction
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