369 research outputs found
Orbital measures in non-equilibrium statistical mechanics: the Onsager relations
We assume that the properties of nonequilibrium stationary states of systems
of particles can be expressed in terms of weighted orbital measures, i.e.
through periodic orbit expansions. This allows us to derive the Onsager
relations for systems of particles subject to a Gaussian thermostat, under
the assumption that the entropy production rate is equal to the phase space
contraction rate. Moreover, this also allows us to prove that the relevant
transport coefficients are not negative. In the appendix we give an argument
for the proper way of treating grazing collisions, a source of possible
singularities in the dynamics.Comment: LaTeX, 14 pages, 1 TeX figure in the tex
The Gallavotti-Cohen Fluctuation Theorem for a non-chaotic model
We test the applicability of the Gallavotti-Cohen fluctuation formula on a
nonequilibrium version of the periodic Ehrenfest wind-tree model. This is a
one-particle system whose dynamics is rather complex (e.g. it appears to be
diffusive at equilibrium), but its Lyapunov exponents are nonpositive. For
small applied field, the system exhibits a very long transient, during which
the dynamics is roughly chaotic, followed by asymptotic collapse on a periodic
orbit. During the transient, the dynamics is diffusive, and the fluctuations of
the current are found to be in agreement with the fluctuation formula, despite
the lack of real hyperbolicity. These results also constitute an example which
manifests the difference between the fluctuation formula and the Evans-Searles
identity.Comment: 12 pages, submitted to Journal of Statistical Physic
Gibbs entropy and irreversible thermodynamics
Recently a number of approaches has been developed to connect the microscopic
dynamics of particle systems to the macroscopic properties of systems in
nonequilibrium stationary states, via the theory of dynamical systems. This way
a direct connection between dynamics and Irreversible Thermodynamics has been
claimed to have been found. However, the main quantity used in these studies is
a (coarse-grained) Gibbs entropy, which to us does not seem suitable, in its
present form, to characterize nonequilibrium states. Various simplified models
have also been devised to give explicit examples of how the coarse-grained
approach may succeed in giving a full description of the Irreversible
Thermodynamics. We analyze some of these models pointing out a number of
difficulties which, in our opinion, need to be overcome in order to establish a
physically relevant connection between these models and Irreversible
Thermodynamics.Comment: 19 pages, 4 eps figures, LaTeX2
The nonequilibrium Ehrenfest gas: a chaotic model with flat obstacles?
It is known that the non-equilibrium version of the Lorentz gas (a billiard
with dispersing obstacles, electric field and Gaussian thermostat) is
hyperbolic if the field is small. Differently the hyperbolicity of the
non-equilibrium Ehrenfest gas constitutes an open problem, since its obstacles
are rhombi and the techniques so far developed rely on the dispersing nature of
the obstacles. We have developed analytical and numerical investigations which
support the idea that this model of transport of matter has both chaotic
(positive Lyapunov exponent) and non-chaotic steady states with a quite
peculiar sensitive dependence on the field and on the geometry, not observed
before. The associated transport behaviour is correspondingly highly irregular,
with features whose understanding is of both theoretical and technological
interest
The Langevin equation for systems with a preferred spatial direction
In this paper, we generalize the theory of Brownian motion and the
Onsager-Machlup theory of fluctuations for spatially symmetric systems to
equilibrium and nonequilibrium steady-state systems with a preferred spatial
direction, due to an external force. To do this, we extend the Langevin
equation to include a bias, which is introduced by the external force and
alters the Gaussian structure of the system's fluctuations. By solving this
extended equation, we demonstrate that the statistical properties of the
fluctuations in these systems can be predicted from physical observables, such
as the temperature and the hydrodynamic gradients.Comment: 1 figur
Note on Phase Space Contraction and Entropy Production in Thermostatted Hamiltonian Systems
The phase space contraction and the entropy production rates of Hamiltonian
systems in an external field, thermostatted to obtain a stationary state are
considered. While for stationary states with a constant kinetic energy the two
rates are formally equal for all numbers of particles N, for stationary states
with constant total (kinetic and potential) energy this only obtains for large
N. However, in both cases a large number of particles is required to obtain
equality with the entropy production rate of Irreversible Thermodynamics.
Consequences of this for the positivity of the transport coefficients and for
the Onsager relations are discussed. Numerical results are presented for the
special case of the Lorentz gas.Comment: 16 pages including 1 table and 3 figures. LaTeX forma
Nonequilibrium Langevin dynamics: a demonstration study of shear flow fluctuations in a simple fluid
The present study is based on a recent success of the second-order stochastic
fluctuation theory in describing time autocorrelations of equilibrium and
nonequilibrium physical systems. In particular, it was shown to yield values of
the related deterministic parameters of the Langevin equation for a Couette
flow in a microscopic Molecular Dynamics model of a simple fluid. In this paper
we find all the remaining constants of the stochastic dynamics, which is then
numerically simulated and directly compared with the original physical system.
By using these data, we study in detail the accuracy and precision of a
second-order Langevin model for nonequilibrium physical systems, theoretically
and computationally. In addition, an intriguing relation is found between an
applied external force and cumulants of the resulting flow fluctuations. This
is characterized by a linear dependence of athermal cumulant ratio, a new
quantity introduced here
Time-dependence of the effective temperatures of a two-dimensional Brownian gyrator with cold and hot components
We consider a model of a two-dimensional molecular machine - called Brownian gyrator - that consists of two coordinates coupled to each other and to separate heat baths at temperatures respectively T x and T y . We consider the limit in which one component is passive, because its bath is 'cold', T x → 0, while the second is in contact with a 'hot' bath, T y > 0, hence it entrains the passive component in a stochastic motion. We derive an asymmetry relation as a function of time, from which time dependent effective temperatures can be obtained for both components. We find that the effective temperature of the passive element tends to a constant value, which is a fraction of T y , while the effective temperature of the driving component grows without bounds, in fact exponentially in time, as the steady-state is approached
Lyapunov spectra and nonequilibrium ensembles equivalence in 2D fluid mechanics
We perform numerical experiments to study the Lyapunov spectra of dynamical
systems associated with the Navier–Stokes (NS) equation in two spatial dimensions truncated over the Fourier basis. Recently new equations, called GNS equations, have been introduced and conjectured to be equivalent to the NS equations at large Reynolds numbers. The Lyapunov spectra of the NS and of the corresponding GNS systems overlap, adding evidence in favor of the conjectured equivalence already studied and partially extended in previous papers. We make use of the Lyapunov spectra to study a fluctuation relation which had been proposed to extend the “fluctuation theorem” to strongly dissipative systems. Preliminary results towards the formulation of a local version of the fluctuation formula are also presented
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