697 research outputs found
The Steady State Fluctuation Relation for the Dissipation Function
We give a proof of transient fluctuation relations for the entropy production
(dissipation function) in nonequilibrium systems, which is valid for most time
reversible dynamics. We then consider the conditions under which a transient
fluctuation relation yields a steady state fluctuation relation for driven
nonequilibrium systems whose transients relax, producing a unique
nonequilibrium steady state. Although the necessary and sufficient conditions
for the production of a unique nonequilibrium steady state are unknown, if such
a steady state exists, the generation of the steady state fluctuation relation
from the transient relation is shown to be very general. It is essentially a
consequence of time reversibility and of a form of decay of correlations in the
dissipation, which is needed also for, e.g., the existence of transport
coefficients. Because of this generality the resulting steady state fluctuation
relation has the same degree of robustness as do equilibrium thermodynamic
equalities. The steady state fluctuation relation for the dissipation stands in
contrast with the one for the phase space compression factor, whose convergence
is problematic, for systems close to equilibrium. We examine some model
dynamics that have been considered previously, and show how they are described
in the context of this work.Comment: 30 pages, 1 figur
On the Fluctuation Relation for Nose-Hoover Boundary Thermostated Systems
We discuss the transient and steady state fluctuation relation for a
mechanical system in contact with two deterministic thermostats at different
temperatures. The system is a modified Lorentz gas in which the fixed
scatterers exchange energy with the gas of particles, and the thermostats are
modelled by two Nos\'e-Hoover thermostats applied at the boundaries of the
system. The transient fluctuation relation, which holds only for a precise
choice of the initial ensemble, is verified at all times, as expected. Times
longer than the mesoscopic scale, needed for local equilibrium to be settled,
are required if a different initial ensemble is considered. This shows how the
transient fluctuation relation asymptotically leads to the steady state
relation when, as explicitly checked in our systems, the condition found in
[D.J. Searles, {\em et al.}, J. Stat. Phys. 128, 1337 (2007)], for the validity
of the steady state fluctuation relation, is verified. For the steady state
fluctuations of the phase space contraction rate \zL and of the dissipation
function \zW, a similar relaxation regime at shorter averaging times is
found. The quantity \zW satisfies with good accuracy the fluctuation relation
for times larger than the mesoscopic time scale; the quantity \zL appears to
begin a monotonic convergence after such times. This is consistent with the
fact that \zW and \zL differ by a total time derivative, and that the tails
of the probability distribution function of \zL are Gaussian.Comment: Major revision. Fig.10 was added. Version to appear in Journal of
Statistical Physic
Dissipative Dicke Model with Collective Atomic Decay: Bistability, Noise-Driven Activation and Non-Thermal First Order Superradiance Transition
The Dicke model describes the coherent interaction of a laser-driven ensemble
of two level atoms with a quantized light field. It is realized within cavity
QED experiments, which in addition to the coherent Dicke dynamics feature
dissipation due to e.g. atomic spontaneous emission and cavity photon loss.
Spontaneous emission supports the uncorrelated decay of individual atomic
excitations as well as the enhanced, collective decay of an excitation that is
shared by atoms and whose strength is determined by the cavity geometry. We
derive a many-body master equation for the dissipative Dicke model including
both spontaneous emission channels and analyze its dynamics on the basis of
Heisenberg-Langevin and stochastic Bloch equations. We find that the collective
loss channel leads to a region of bistability between the empty and the
superradiant state. Transitions between these states are driven by non-thermal,
markovian noise. The interplay between dissipative and coherent elements leads
to a genuine non-equilibrium dynamics in the bistable regime, which is
expressed via a non-conservative force and a multiplicative noise kernel
appearing in the stochastic Bloch equations. We present a semiclassical
approach, based on stochastic nonlinear optical Bloch equations, which for the
infinite-range Dicke Model become exact in the large--limit. The absence of
an effective free energy functional, however, necessitates to include
fluctuation corrections with for finite to locate
the non-thermal first-order phase transition between the superradiant and the
empty cavity.Comment: as published in Physical Review
Fluctuations and response in a non-equilibrium micron-sized system
The linear response of non-equilibrium systems with Markovian dynamics
satisfies a generalized fluctuation-dissipation relation derived from time
symmetry and antisymmetry properties of the fluctuations. The relation involves
the sum of two correlation functions of the observable of interest: one with
the entropy excess and the second with the excess of dynamical activity with
respect to the unperturbed process, without recourse to anything but the
dynamics of the system. We illustrate this approach in the experimental
determination of the linear response of the potential energy of a Brownian
particle in a toroidal optical trap. The overdamped particle motion is
effectively confined to a circle, undergoing a periodic potential and driven
out of equilibrium by a non-conservative force. Independent direct and indirect
measurements of the linear response around a non-equilibrium steady state are
performed in this simple experimental system. The same ideas are applicable to
the measurement of the response of more general non-equilibrium micron-sized
systems immersed in Newtonian fluids either in stationary or non-stationary
states and possibly including inertial degrees of freedom.Comment: 12 pages, submitted to J. Stat. Mech., revised versio
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