13 research outputs found
Work distribution for the driven harmonic oscillator with time-dependent strength: Exact solution and slow driving
We study the work distribution of a single particle moving in a harmonic
oscillator with time-dependent strength. This simple system has a non-Gaussian
work distribution with exponential tails. The time evolution of the
corresponding moment generating function is given by two coupled ordinary
differential equations that are solved numerically. Based on this result we
study the behavior of the work distribution in the limit of slow but finite
driving and show that it approaches a Gaussian distribution arbitrarily well
Fluctuation relations for heat engines in time-periodic steady states
A fluctuation relation for heat engines (FRHE) has been derived recently. In
the beginning, the system is in contact with the cooler bath. The system is
then coupled to the hotter bath and external parameters are changed cyclically,
eventually bringing the system back to its initial state, once the coupling
with the hot bath is switched off. In this work, we lift the condition of
initial thermal equilibrium and derive a new fluctuation relation for the
central system (heat engine) being in a time-periodic steady state (TPSS).
Carnot's inequality for classical thermodynamics follows as a direct
consequence of this fluctuation theorem even in TPSS. For the special cases of
the absence of hot bath and no extraction of work, we obtain the integral
fluctuation theorem for total entropy and the generalized exchange fluctuation
theorem, respectively. Recently microsized heat engines have been realized
experimentally in the TPSS. We numerically simulate the same model and verify
our proposed theorems.Comment: 9 page
Influence of rotational force fields on the determination of the work done on a driven Brownian particle
For a Brownian system the evolution of thermodynamic quantities is a
stochastic process. In particular, the work performed on a driven colloidal
particle held in an optical trap changes for each realization of the
experimental manipulation, even though the manipulation protocol remains
unchanged. Nevertheless, the work distribution is governed by established laws.
Here, we show how the measurement of the work distribution is influenced by the
presence of rotational, i.e. nonconservative, radiation forces. Experiments on
particles of different materials show that the rotational radiation forces, and
therefore their effect on the work distributions, increase with the particle
refractive index.Comment: 12 pages, 4 figure
Estimate of the free energy difference in mechanical systems from work fluctuations: experiments and models
The work fluctuations of an oscillator in contact with a heat reservoir and
driven out of equilibrium by an external force are studied experimentally. The
oscillator dynamics is modeled by a Langevin equation. We find both
experimentally and theoretically that, if the driving force does not change the
equilibrium properties of the thermal fluctuations of this mechanical system,
the free energy difference between two equilibrium states can be
exactly computed using the Jarzynski equality (JE) and the Crooks relation (CR)
\cite{jarzynski1, crooks1, jarzynski2}, independently of the time scale and
amplitude of the driving force. The applicability limits for the JE and CR at
very large driving forces are discussed. Finally, when the work fluctuations
are Gaussian, we propose an alternative empirical method to compute
which can be safely applied, even in cases where the JE and CR might not hold.
The results of this paper are useful to compute in complex systems
such as the biological ones.Comment: submitted to Journal of Statistical Mechanics: Theory and experimen
Feynman's ratchet and pawl: an exactly solvable model
We introduce a simple, discrete model of Feynman's ratchet and pawl,
operating between two heat reservoirs. We solve exactly for the steady-state
directed motion and heat flows produced, first in the absence and then in the
presence of an external load. We show that the model can act both as a heat
engine and as a refrigerator. We finally investigate the behavior of the system
near equilibrium, and use our model to confirm general predictions based on
linear response theory.Comment: 19 pages + 10 figures; somewhat tighter presentatio
Work and heat fluctuations in two-state systems: a trajectory thermodynamics formalism
Two-state models provide phenomenological descriptions of many different
systems, ranging from physics to chemistry and biology. We investigate work
fluctuations in an ensemble of two-state systems driven out of equilibrium
under the action of an external perturbation. We calculate the probability
density P(W) that a work equal to W is exerted upon the system along a given
non-equilibrium trajectory and introduce a trajectory thermodynamics formalism
to quantify work fluctuations in the large-size limit. We then define a
trajectory entropy S(W) that counts the number of non-equilibrium trajectories
P(W)=exp(S(W)/kT) with work equal to W. A trajectory free-energy F(W) can also
be defined, which has a minimum at a value of the work that has to be
efficiently sampled to quantitatively test the Jarzynski equality. Within this
formalism a Lagrange multiplier is also introduced, the inverse of which plays
the role of a trajectory temperature. Our solution for P(W) exactly satisfies
the fluctuation theorem by Crooks and allows us to investigate
heat-fluctuations for a protocol that is invariant under time reversal. The
heat distribution is then characterized by a Gaussian component (describing
small and frequent heat exchange events) and exponential tails (describing the
statistics of large deviations and rare events). For the latter, the width of
the exponential tails is related to the aforementioned trajectory temperature.
Finite-size effects to the large-N theory and the recovery of work
distributions for finite N are also discussed. Finally, we pay particular
attention to the case of magnetic nanoparticle systems under the action of a
magnetic field H where work and heat fluctuations are predicted to be
observable in ramping experiments in micro-SQUIDs.Comment: 28 pages, 14 figures (Latex
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
Single-molecule experiments in biological physics: methods and applications
I review single-molecule experiments (SME) in biological physics. Recent
technological developments have provided the tools to design and build
scientific instruments of high enough sensitivity and precision to manipulate
and visualize individual molecules and measure microscopic forces. Using SME it
is possible to: manipulate molecules one at a time and measure distributions
describing molecular properties; characterize the kinetics of biomolecular
reactions and; detect molecular intermediates. SME provide the additional
information about thermodynamics and kinetics of biomolecular processes. This
complements information obtained in traditional bulk assays. In SME it is also
possible to measure small energies and detect large Brownian deviations in
biomolecular reactions, thereby offering new methods and systems to scrutinize
the basic foundations of statistical mechanics. This review is written at a
very introductory level emphasizing the importance of SME to scientists
interested in knowing the common playground of ideas and the interdisciplinary
topics accessible by these techniques. The review discusses SME from an
experimental perspective, first exposing the most common experimental
methodologies and later presenting various molecular systems where such
techniques have been applied. I briefly discuss experimental techniques such as
atomic-force microscopy (AFM), laser optical tweezers (LOT), magnetic tweezers
(MT), biomembrane force probe (BFP) and single-molecule fluorescence (SMF). I
then present several applications of SME to the study of nucleic acids (DNA,
RNA and DNA condensation), proteins (protein-protein interactions, protein
folding and molecular motors). Finally, I discuss applications of SME to the
study of the nonequilibrium thermodynamics of small systems and the
experimental verification of fluctuation theorems. I conclude with a discussion
of open questions and future perspectives.Comment: Latex, 60 pages, 12 figures, Topical Review for J. Phys. C (Cond.
Matt