91 research outputs found

### Non-equilibrium Thermodynamics and Fluctuations

In the last ten years, a number of ``Conventional Fluctuation Theorems'' have
been derived for systems with deterministic or stochastic dynamics, in a
transient or in a non-equilibrium stationary state. These theorems gave
explicit expressions for the ratio of the probability to find the system with a
certain value of entropy (or heat) production to that of finding the opposite
value. A similar theorem for the fluctuations of the work done on a system has
recently been demonstrated experimentally for a simple system in a transient
state, consisting of a Brownian particle in water, confined by a moving
harmonic potential. In this paper we show that because of the interaction
between the stochastic motion of the particle in water and its deterministic
motion in the potential, very different new heat theorems are found than in the
conventional case. One of the consequences of these new heat Fluctuation
Theorems is that the ratio of the probability for the Brownian particle to
absorb heat from rather than supply heat to the water is much larger than in
the Conventional Fluctuation Theorem. This could be of relevance for
micro/nano-technology.Comment: 10 pages, 6 figures. Some corrections in the text were made.
Submitted to Physica

### Long time diffusion in suspensions of interacting charged colloids

A new expression is given for the long time diffusion coefficient DL(k) of charged interacting colloidal spheres in suspension, as a function of the wavenumber k, near k = km, where the static structure factor has a maximum. The expression is based on a physical analogy between a mode description of the behaviour of atomic fluids (as observed in neutron scattering) and of colloids (as observed in light scattering). Use of this expresssion in conjunction with a hard-sphere model yields good agreement with extant data on colloids

### Short-time fluctuations of displacements and work

A recent theorem giving the initial behavior of very short-time fluctuations
of particle displacements in classical many-body systems is discussed. It has
applications to equilibrium and non-equilibrium systems, one of which is a
series expansion of the distribution of work fluctuations around a Gaussian
function. To determine the time-scale at which this series expansion is valid,
we present preliminary numerical results for a Lennard-Jones fluid. These
results suggest that the series expansion converges up to time scales on the
order of a picosecond, below which a simple Gaussian function for the
distribution of the displacements can be used.Comment: 10 pages, 3 figure

### Superstatistics

We consider nonequilibrium systems with complex dynamics in stationary states
with large fluctuations of intensive quantities (e.g. the temperature, chemical
potential, or energy dissipation) on long time scales. Depending on the
statistical properties of the fluctuations, we obtain different effective
statistical mechanics descriptions. Tsallis statistics is one, but other
classes of generalized statistics are obtained as well. We show that for small
variance of the fluctuations all these different statistics behave in a
universal way.Comment: 12 pages /a few more references and comments added in revised versio

### Theorem on the Distribution of Short Time Single Particle Displacements

The distribution of the initial very short-time displacements of a single
particle is considered for a class of classical systems with Gaussian initial
velocity distributions and arbitrary initial particle positions. A very brief
sketch is given of a rather intricate and lengthy proof that for this class of
systems the nth order cumulants behave as t^{2n} for all n>2, rather than as
t^{n}. We also briefly discuss some physical consequences for liquids.Comment: Short 8 page pedagogical review of cond-mat/0505734 for Proc. of
"News, Expectations and Trends in Statistical Physics", Crete 200

### On first-order phase transition in microcanonical and canonical non-extensive systems

Two examples of Microcanonical Potts models, 2-dimensional nearest neighbor
and mean field, are considered via exact enumeration of states and analytical
asymptotic methods. In the interval of energies corresponding to a first order
phase transition, both of these models exhibit a convex dip in the entropy vs
energy plot and a region with negative specific heat within the dip. It is
observed that in the nearest neighbor model the dip flattens and disappears as
the lattice size grows, while in the mean field model the dip persists even in
the limit of an infinite system. If formal transitions from microcanonical to
canonical ensembles and back are performed for an infinite but non-extensive
system, the convex dip in the microcanonical entropy plot disappears.Comment: 10 pages, 8 figure

### Superstatistical generalization of the work fluctuation theorem

We derive a generalized version of the work fluctuation theorem for
nonequilibrium systems with spatio-temporal temperature fluctuations. For
chi-square distributed inverse temperature we obtain a generalized fluctuation
theorem based on q-exponentials, whereas for other temperature distributions
more complicated formulae arise. Since q-exponentials have a power law decay,
the decay rate in this generalized fluctuation theorem is much slower than the
conventional exponential decay. This implies that work fluctuations can be of
relevance for the design of micro and nano structures, since the work done on
the system is relatively much larger than in the conventional fluctuation
theorem.Comment: 13 pages. Contribution to the Proceedings of `Trends and Perspectives
in Extensive and Nonextensive Statistical Mechanics', in honour of
Constantino Tsallis' 60th birthday (to appear in Physica A

### Stationary and Transient Work-Fluctuation Theorems for a Dragged Brownian Particle

Recently Wang et al. carried out a laboratory experiment, where a Brownian
particle was dragged through a fluid by a harmonic force with constant velocity
of its center. This experiment confirmed a theoretically predicted work related
integrated (I) Transient Fluctuation Theorem (ITFT), which gives an expression
for the ratio for the probability to find positive or negative values for the
fluctuations of the total work done on the system in a given time in a
transient state. The corresponding integrated stationary state fluctuation
theorem (ISSFT) was not observed. Using an overdamped Langevin equation and an
arbitrary motion for the center of the harmonic force, all quantities of
interest for these theorems and the corresponding non-integrated ones (TFT and
SSFT, resp.) are theoretically explicitly obtained in this paper. While the
(I)TFT is satisfied for all times, the (I)SSFT only holds asymptotically in
time. Suggestions for further experiments with arbitrary velocity of the
harmonic force and in which also the ISSFT could be observed, are given. In
addition, a non-trivial long-time relation between the ITFT and the ISSFT was
discovered, which could be observed experimentally, especially in the case of a
resonant circular motion of the center of the harmonic force.Comment: 20 pages, 3 figure

### Hydrodynamics of probabilistic ballistic annihilation

We consider a dilute gas of hard spheres in dimension $d \geq 2$ that upon
collision either annihilate with probability $p$ or undergo an elastic
scattering with probability $1-p$. For such a system neither mass, momentum,
nor kinetic energy are conserved quantities. We establish the hydrodynamic
equations from the Boltzmann equation description. Within the Chapman-Enskog
scheme, we determine the transport coefficients up to Navier-Stokes order, and
give the closed set of equations for the hydrodynamic fields chosen for the
above coarse grained description (density, momentum and kinetic temperature).
Linear stability analysis is performed, and the conditions of stability for the
local fields are discussed.Comment: 19 pages, 3 eps figures include

### Fluctuation formula for nonreversible dynamics in the thermostated Lorentz gas

We investigate numerically the validity of the Gallavotti-Cohen fluctuation
formula in the two and three dimensional periodic Lorentz gas subjected to
constant electric and magnetic fields and thermostated by the Gaussian
isokinetic thermostat. The magnetic field breaks the time reversal symmetry,
and by choosing its orientation with respect to the lattice one can have either
a generalized reversing symmetry or no reversibility at all. Our results
indicate that the scaling property described by the fluctuation formula may be
approximately valid for large fluctuations even in the absence of
reversibility.Comment: 6 pages, 6 figure

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