242 research outputs found
Heat flow in chains driven by thermal noise
We consider the large deviation function for a classical harmonic chain
composed of N particles driven at the end points by heat reservoirs, first
derived in the quantum regime by Saito and Dhar and in the classical regime by
Saito and Dhar and Kundu et al. Within a Langevin description we perform this
calculation on the basis of a standard path integral calculation in Fourier
space. The cumulant generating function yielding the large deviation function
is given in terms of a transmission Green's function and is consistent with the
fluctuation theorem. We find a simple expression for the tails of the heat
distribution which turn out to decay exponentially. We, moreover, consider an
extension of a single particle model suggested by Derrida and Brunet and
discuss the two-particle case. We also discuss the limit for large N and
present a closed expression for the cumulant generating function. Finally, we
present a derivation of the fluctuation theorem on the basis of a Fokker-Planck
description. This result is not restricted to the harmonic case but is valid
for a general interaction potential between the particles.Comment: Latex: 26 pages and 9 figures, appeared in J. Stat. Mech. P04005
(2012
Work probability distribution in single molecule experiments
We derive and solve a differential equation satisfied by the probability
distribution of the work done on a single biomolecule in a mechanical unzipping
experiment. The unzipping is described as a thermally activated escape process
in an energy landscape. The Jarzynski equality is recovered as an identity,
independent of the pulling protocol. This approach allows one to evaluate
easily, by numerical integration, the work distribution, once a few parameters
of the energy landscape are known.Comment: To appear on EP
An Ising-Like model for protein mechanical unfolding
The mechanical unfolding of proteins is investigated by extending the
Wako-Saito-Munoz-Eaton model, a simplified protein model with binary degrees of
freedom, which has proved successful in describing the kinetics of protein
folding. Such a model is generalized by including the effect of an external
force, and its thermodynamics turns out to be exactly solvable. We consider two
molecules, the 27th immunoglobulin domain of titin and protein PIN1. In the
case of titin we determine equilibrium force-extension curves and study
nonequilibrium phenomena in the frameworks of dynamic loading and force clamp
protocols, verifying theoretical laws and finding the position of the kinetic
barrier which hinders the unfolding of the molecule. The PIN1 molecule is used
to check the possibility of computing the free energy landscape as a function
of the molecule length by means of an extended form of the Jarzynski equality.Comment: 4 pages + appendi
Energetics and performance of a microscopic heat engine based on exact calculations of work and heat distributions
We investigate a microscopic motor based on an externally controlled
two-level system. One cycle of the motor operation consists of two strokes.
Within each stroke, the two-level system is in contact with a given thermal
bath and its energy levels are driven with a constant rate. The time evolution
of the occupation probabilities of the two states are controlled by one rate
equation and represent the system's response with respect to the external
driving. We give the exact solution of the rate equation for the limit cycle
and discuss the emerging thermodynamics: the work done on the environment, the
heat exchanged with the baths, the entropy production, the motor's efficiency,
and the power output. Furthermore we introduce an augmented stochastic process
which reflects, at a given time, both the occupation probabilities for the two
states and the time spent in the individual states during the previous
evolution. The exact calculation of the evolution operator for the augmented
process allows us to discuss in detail the probability density for the
performed work during the limit cycle. In the strongly irreversible regime, the
density exhibits important qualitative differences with respect to the more
common Gaussian shape in the regime of weak irreversibility.Comment: 21 pages, 7 figure
Aging in lattice-gas models with constrained dynamics
We investigate the aging behavior of lattice-gas models with constrained
dynamics in which particle exchange with a reservoir is allowed. Such models
provide a particularly simple interpretation of aging phenomena as a slow
approach to criticality. They appear as the simplest three dimensional models
exhibiting a glassy behavior similar to that of mean field (low temperature
mode-coupling) models.Comment: 5 pages and 3 figures, REVTeX. Submitted to Europhysics Letter
Discrete Breathers in a Realistic Coarse-Grained Model of Proteins
We report the results of molecular dynamics simulations of an off-lattice
protein model featuring a physical force-field and amino-acid sequence. We show
that localized modes of nonlinear origin (discrete breathers) emerge naturally
as continuations of a subset of high-frequency normal modes residing at
specific sites dictated by the native fold. In the case of the small
-barrel structure that we consider, localization occurs on the turns
connecting the strands. At high energies, discrete breathers stabilize the
structure by concentrating energy on few sites, while their collapse marks the
onset of large-amplitude fluctuations of the protein. Furthermore, we show how
breathers develop as energy-accumulating centres following perturbations even
at distant locations, thus mediating efficient and irreversible energy
transfers. Remarkably, due to the presence of angular potentials, the breather
induces a local static distortion of the native fold. Altogether, the
combination of this two nonlinear effects may provide a ready means for
remotely controlling local conformational changes in proteins.Comment: Submitted to Physical Biolog
Entropy production for mechanically or chemically driven biomolecules
Entropy production along a single stochastic trajectory of a biomolecule is
discussed for two different sources of non-equilibrium. For a molecule
manipulated mechanically by an AFM or an optical tweezer, entropy production
(or annihilation) occurs in the molecular conformation proper or in the
surrounding medium. Within a Langevin dynamics, a unique identification of
these two contributions is possible. The total entropy change obeys an integral
fluctuation theorem and a class of further exact relations, which we prove for
arbitrarily coupled slow degrees of freedom including hydrodynamic
interactions. These theoretical results can therefore also be applied to driven
colloidal systems. For transitions between different internal conformations of
a biomolecule involving unbalanced chemical reactions, we provide a
thermodynamically consistent formulation and identify again the two sources of
entropy production, which obey similar exact relations. We clarify the
particular role degenerate states have in such a description
Non-Boltzmann stationary distributions and nonequilibrium relations in active baths
Most natural and engineered processes, such as biomolecular reactions, protein folding, and population dynamics, occur far from equilibrium and therefore cannot be treated within the framework of classical equilibrium thermodynamics. Here we experimentally study how some fundamental thermodynamic quantities and relations are affected by the presence of the nonequilibrium fluctuations associated with an active bath. We show in particular that, as the confinement of the particle increases, the stationary probability distribution of a Brownian particle confined within a harmonic potential becomes non-Boltzmann, featuring a transition from a Gaussian distribution to a heavy-tailed distribution. Because of this, nonequilibrium relations (e.g., the Jarzynski equality and Crooks fluctuation theorem) cannot be applied. We show that these relations can be restored by using the effective potential associated with the stationary probability distribution. We corroborate our experimental findings with theoretical arguments. © 2016 American Physical Society
Fluctuations of the total entropy production in stochastic systems
Fluctuations of the excess heat in an out of equilibrium steady state are
experimentally investigated in two stochastic systems : an electric circuit
with an imposed mean current and a harmonic oscillator driven out of
equilibrium by a periodic torque. In these two linear systems, we study excess
heat that represents the difference between the dissipated heat out of
equilibrium and the dissipated heat at equilibrium. Fluctuation theorem holds
for the excess heat in the two experimental systems for all observation times
and for all fluctuation magnitudes.Comment: 6
Heat release by controlled continuous-time Markov jump processes
We derive the equations governing the protocols minimizing the heat released
by a continuous-time Markov jump process on a one-dimensional countable state
space during a transition between assigned initial and final probability
distributions in a finite time horizon. In particular, we identify the
hypotheses on the transition rates under which the optimal control strategy and
the probability distribution of the Markov jump problem obey a system of
differential equations of Hamilton-Bellman-Jacobi-type. As the state-space mesh
tends to zero, these equations converge to those satisfied by the diffusion
process minimizing the heat released in the Langevin formulation of the same
problem. We also show that in full analogy with the continuum case, heat
minimization is equivalent to entropy production minimization. Thus, our
results may be interpreted as a refined version of the second law of
thermodynamics.Comment: final version, section 2.1 revised, 26 pages, 3 figure
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