1,567 research outputs found
The fluctuation theorem and Lyapunov weights
The Fluctuation Theorem (FT) is a generalisation of the Second Law of
Thermodynamics that applies to small systems observed for short times. For
thermostatted systems it gives the probability ratio that entropy will be
consumed rather than produced. In this paper we derive the Transient and Steady
State Fluctuation Theorems using Lyapunov weights rather than the usual Gibbs
weights. At long times the Fluctuation Theorems so derived are identical to
those derived using the more standard Gibbs weights.Comment: 26 pages; to appear in Physica
Ensemble Dependence of the Transient Fluctuation Theorem
The Fluctuation Theorem gives an analytical expression for the probability of
observing second law violating dynamical fluctuations, in nonequilibrium
systems. At equilibrium statistical mechanical fluctuations are known to be
ensemble dependent. In this paper we generalise the Transient and Steady State
Fluctuation Theorems to various nonequilibrium dynamical ensembles. The
Transient and Steady State Fluctuation Theorem for an isokinetic ensemble of
isokinetic trajectories is tested using nonequilibrium molecular dynamics
simulations of shear flow.We would like to thank the Australian Research Council
for the support of this project
The Fluctuation Theorem and Green-Kubo Relations
Green-Kubo and Einstein expressions for the transport coefficients of a fluid
in a nonequilibrium steady state can be derived using the Fluctuation Theorem
and by assuming the probability distribution of the time-averaged dissipative
flux is Gaussian. These expressions are consistent with those obtained using
linear response theory and are valid in the linear regime. It is shown that
these expressions are however, not valid in the nonlinear regime where the
fluid is driven far from equilibrium. We advance an argument for why these
expression are only valid in the linear response, zero field limit.Comment: 32 pages, inc. 6 figures Discussion and notation improve
Ensemble Dependence of the Transient Fluctuation Theorem
The Fluctuation Theorem gives an analytical expression for the probability of
observing second law violating dynamical fluctuations, in nonequilibrium
systems. At equilibrium statistical mechanical fluctuations are known to be
ensemble dependent. In this paper we generalise the Transient and Steady State
Fluctuation Theorems to various nonequilibrium dynamical ensembles. The
Transient and Steady State Fluctuation Theorem for an isokinetic ensemble of
isokinetic trajectories is tested using nonequilibrium molecular dynamics
simulations of shear flow.Comment: 16 pages, 1 table, 4 figures; presentation of generalised formulae
and discussion clarifie
A local fluctuation theorem for large systems
The fluctuation theorem characterizes the distribution of the dissipation in
nonequilibrium systems and proves that the average dissipation will be
positive. For a large system with no external source of fluctuation,
fluctuations in properties will become unobservable and details of the
fluctuation theorem are unable to be explored. In this letter, we consider such
a situation and show how a fluctuation theorem can be obtained for a small open
subsystem within the large system. We find that a correction term has to be
added to the large system fluctuation theorem due to correlation of the
subsystem with the surroundings. Its analytic expression can be derived
provided some general assumptions are fulfilled, and its relevance it checked
using numerical simulations.Comment: 5 pages, 5 figures; revised and supplementary material include
Generalised Fluctuation Formula
We develop a General Fluctuation Formula for phase variables that are odd
under time reversal. Simulations are used to verify the new formula.Comment: 10 pages, 5 figures, submitted to Procedings of the 3rd Tohwa
University International Conference of Statistical Physics, Nov 8-12, 1999
(AIP Conferences Series
On the Application of the Gallavotti-Cohen Fluctuation Relation to Thermostatted Steady States Near Equilibrium
The fluctuation relation of the Gallavotti-Cohen Fluctuation Theorem (GCFT)
concerns fluctuations in the phase space compression rate of dissipative,
reversible dynamical systems. It has been proven for Anosov systems, but it is
expected to apply more generally. This raises the question of which non-Anosov
systems satisfy the fluctuation relation. We analyze time dependent
fluctuations in the phase space compression rate of a class of N-particle
systems that are at equilibrium or in near equilibrium steady states. This
class does not include Anosov systems or isoenergetic systems, however, it
includes most steady state systems considered in molecular dynamics simulations
of realistic systems. We argue that the fluctuations of the phase space
compression rate of these systems at or near equilibrium do not satisfy the
fluctuation relation of the GCFT, although the discrepancies become somewhat
smaller as the systems move further from equilibrium. In contrast, similar
fluctuation relations for an appropriately defined dissipation function appear
to hold both near and far from equilibrium.Comment: 46 pages, for publication in PR
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