4 research outputs found
Onsager-Machlup theory for nonequilibrium steady states and fluctuation theorems
A generalization of the Onsager-Machlup theory from equilibrium to
nonequilibrium steady states and its connection with recent fluctuation
theorems are discussed for a dragged particle restricted by a harmonic
potential in a heat reservoir. Using a functional integral approach, the
probability functional for a path is expressed in terms of a Lagrangian
function from which an entropy production rate and dissipation functions are
introduced, and nonequilibrium thermodynamic relations like the energy
conservation law and the second law of thermodynamics are derived. Using this
Lagrangian function we establish two nonequilibrium detailed balance relations,
which not only lead to a fluctuation theorem for work but also to one related
to energy loss by friction. In addition, we carried out the functional
integrals for heat explicitly, leading to the extended fluctuation theorem for
heat. We also present a simple argument for this extended fluctuation theorem
in the long time limit.Comment: 20 pages, 2 figure
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
Fluctuation Relations for Diffusion Processes
The paper presents a unified approach to different fluctuation relations for
classical nonequilibrium dynamics described by diffusion processes. Such
relations compare the statistics of fluctuations of the entropy production or
work in the original process to the similar statistics in the time-reversed
process. The origin of a variety of fluctuation relations is traced to the use
of different time reversals. It is also shown how the application of the
presented approach to the tangent process describing the joint evolution of
infinitesimally close trajectories of the original process leads to a
multiplicative extension of the fluctuation relations.Comment: 38 page