4,105 research outputs found
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
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
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
Statistical Mechanics of Time Independent Non-Dissipative Nonequilibrium States
We examine the question of whether the formal expressions of equilibrium
statistical mechanics can be applied to time independent non-dissipative
systems that are not in true thermodynamic equilibrium and are nonergodic. By
assuming the phase space may be divided into time independent, locally ergodic
domains, we argue that within such domains the relative probabilities of
microstates are given by the standard Boltzmann weights. In contrast to
previous energy landscape treatments, that have been developed specifically for
the glass transition, we do not impose an a priori knowledge of the
inter-domain population distribution. Assuming that these domains are robust
with respect to small changes in thermodynamic state variables we derive a
variety of fluctuation formulae for these systems. We verify our theoretical
results using molecular dynamics simulations on a model glass forming system.
Non-equilibrium Transient Fluctuation Relations are derived for the
fluctuations resulting from a sudden finite change to the system's temperature
or pressure and these are shown to be consistent with the simulation results.
The necessary and sufficient conditions for these relations to be valid are
that the domains are internally populated by Boltzmann statistics and that the
domains are robust. The Transient Fluctuation Relations thus provide an
independent quantitative justification for the assumptions used in our
statistical mechanical treatment of these systems.Comment: 17 pages, 4 figures, minor amendment
New observations regarding deterministic, time reversible thermostats and Gauss's principle of least constraint
Deterministic thermostats are frequently employed in non-equilibrium
molecular dynamics simulations in order to remove the heat produced
irreversibly over the course of such simulations. The simplest thermostat is
the Gaussian thermostat, which satisfies Gauss's principle of least constraint
and fixes the peculiar kinetic energy. There are of course infinitely many ways
to thermostat systems, e.g. by fixing . In
the present paper we provide, for the first time, convincing arguments as to
why the conventional Gaussian isokinetic thermostat () is unique in this
class. We show that this thermostat minimizes the phase space compression and
is the only thermostat for which the conjugate pairing rule (CPR) holds.
Moreover it is shown that for finite sized systems in the absence of an applied
dissipative field, all other thermostats () perform work on the system
in the same manner as a dissipative field while simultaneously removing the
dissipative heat so generated. All other thermostats () are thus
auto-dissipative. Among all -thermostats, only the Gaussian
thermostat permits an equilibrium state.Comment: 27 pages including 10 figures; submitted for publication Journal of
Chemical Physic
The rheology of solid glass
As the glass transition is approached from the high temperature side, viewed as a liquid, the properties of the ever more viscous supercooled liquid are continuous functions of temperature and pressure. The point at which we decide to classify the fluid as a solid is therefore subjective. This subjective decision does, however, have discontinuous consequences for how we determine the rheological properties of the glass. We apply the recently discovered relaxation theorem to the time independent, nondissipative, nonergodic glassy state to derive an expression for the phase space distribution of an ensemble of glass samples. This distribution is then used to construct a time dependent linear response theory for aged glassysolids. The theory is verified using molecular dynamics simulations of oscillatory shear for a realistic model glass former with excellent agreement being obtained between the response theory calculations and direct nonequilibrium molecular dynamics calculations. Our numerical results confirm that unlike all the fluid states, including supercooled liquids, a solidglass (in common with crystalline states) has a nonzero value for the zero frequency shear modulus. Of all the states of matter, a supercooled fluid approaching the glass transition has the highest value for the limiting zero frequency shear viscosity. Finally, solidglasses like dilute gases and crystals have a positive temperature coefficient for the shear viscosity whereas supercooled and normal liquids have a negative temperature coefficient.We thank the National Computational Infrastructure
NCI for computational facilities and the Australian
Research Council ARC for funding
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
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
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