333 research outputs found
On the nonequilibrium entropy of large and small systems
Thermodynamics makes definite predictions about the thermal behavior of
macroscopic systems in and out of equilibrium. Statistical mechanics aims to
derive this behavior from the dynamics and statistics of the atoms and
molecules making up these systems. A key element in this derivation is the
large number of microscopic degrees of freedom of macroscopic systems.
Therefore, the extension of thermodynamic concepts, such as entropy, to small
(nano) systems raises many questions. Here we shall reexamine various
definitions of entropy for nonequilibrium systems, large and small. These
include thermodynamic (hydrodynamic), Boltzmann, and Gibbs-Shannon entropies.
We shall argue that, despite its common use, the last is not an appropriate
physical entropy for such systems, either isolated or in contact with thermal
reservoirs: physical entropies should depend on the microstate of the system,
not on a subjective probability distribution. To square this point of view with
experimental results of Bechhoefer we shall argue that the Gibbs-Shannon
entropy of a nano particle in a thermal fluid should be interpreted as the
Boltzmann entropy of a dilute gas of Brownian particles in the fluid
A Fresh Look at Entropy and the Second Law of Thermodynamics
This paper is a non-technical, informal presentation of our theory of the
second law of thermodynamics as a law that is independent of statistical
mechanics and that is derivable solely from certain simple assumptions about
adiabatic processes for macroscopic systems. It is not necessary to assume
a-priori concepts such as "heat", "hot and cold", "temperature". These are
derivable from entropy, whose existence we derive from the basic assumptions.
See cond-mat/9708200 and math-ph/9805005.Comment: LaTex file. To appear in the April 2000 issue of PHYSICS TODA
Sum of exit times in series of metastable states in probabilistic cellular automata
Reversible Probabilistic Cellular Automata are a special class
of automata whose stationary behavior is described by Gibbs--like
measures. For those models the dynamics can be trapped for a very
long time in states which are very different from the ones typical
of stationarity.
This phenomenon can be recasted in the framework of metastability
theory which is typical of Statistical Mechanics.
In this paper we consider a model presenting two not degenerate in
energy
metastable states which form a series, in the sense that,
when the dynamics is started at one of them, before reaching
stationarity, the system must necessarily visit the second one.
We discuss a rule for combining the exit times
from each of the metastable states
Optimal leverage from non-ergodicity
In modern portfolio theory, the balancing of expected returns on investments
against uncertainties in those returns is aided by the use of utility
functions. The Kelly criterion offers another approach, rooted in information
theory, that always implies logarithmic utility. The two approaches seem
incompatible, too loosely or too tightly constraining investors' risk
preferences, from their respective perspectives. The conflict can be understood
on the basis that the multiplicative models used in both approaches are
non-ergodic which leads to ensemble-average returns differing from time-average
returns in single realizations. The classic treatments, from the very beginning
of probability theory, use ensemble-averages, whereas the Kelly-result is
obtained by considering time-averages. Maximizing the time-average growth rates
for an investment defines an optimal leverage, whereas growth rates derived
from ensemble-average returns depend linearly on leverage. The latter measure
can thus incentivize investors to maximize leverage, which is detrimental to
time-average growth and overall market stability. The Sharpe ratio is
insensitive to leverage. Its relation to optimal leverage is discussed. A
better understanding of the significance of time-irreversibility and
non-ergodicity and the resulting bounds on leverage may help policy makers in
reshaping financial risk controls.Comment: 17 pages, 3 figures. Updated figures and extended discussion of
ergodicit
The phonon theory of liquid thermodynamics
Heat capacity of matter is considered to be its most important property
because it holds information about system's degrees of freedom as well as the
regime in which the system operates, classical or quantum. Heat capacity is
well understood in gases and solids but not in the third state of matter,
liquids, and is not discussed in physics textbooks as a result. The perceived
difficulty is that interactions in a liquid are both strong and
system-specific, implying that the energy strongly depends on the liquid type
and that, therefore, liquid energy can not be calculated in general form. Here,
we develop a phonon theory of liquids where this problem is avoided. The theory
covers both classical and quantum regimes. We demonstrate good agreement of
calculated and experimental heat capacity of 21 liquids, including noble,
metallic, molecular and hydrogen-bonded network liquids in a wide range of
temperature and pressure.Comment: 7 pages, 4 figure
Conditioned stochastic particle systems and integrable quantum spin systems
We consider from a microscopic perspective large deviation properties of
several stochastic interacting particle systems, using their mapping to
integrable quantum spin systems. A brief review of recent work is given and
several new results are presented: (i) For the general disordered symmectric
exclusion process (SEP) on some finite lattice conditioned on no jumps into
some absorbing sublattice and with initial Bernoulli product measure with
density we prove that the probability of no absorption event
up to microscopic time can be expressed in terms of the generating function
for the particle number of a SEP with particle injection and empty initial
lattice. Specifically, for the symmetric simple exclusion process on conditioned on no jumps into the origin we obtain the explicit first and
second order expansion in of and also to first order in
the optimal microscopic density profile under this conditioning. For the
disordered ASEP on the finite torus conditioned on a very large current we show
that the effective dynamics that optimally realizes this rare event does not
depend on the disorder, except for the time scale. For annihilating and
coalescing random walkers we obtain the generating function of the number of
annihilated particles up to time , which turns out to exhibit some universal
features.Comment: 25 page
Dynamics and transport near quantum-critical points
The physics of non-zero temperature dynamics and transport near
quantum-critical points is discussed by a detailed study of the O(N)-symmetric,
relativistic, quantum field theory of a N-component scalar field in spatial
dimensions. A great deal of insight is gained from a simple, exact solution of
the long-time dynamics for the N=1 d=1 case: this model describes the critical
point of the Ising chain in a transverse field, and the dynamics in all the
distinct, limiting, physical regions of its finite temperature phase diagram is
obtained. The N=3, d=1 model describes insulating, gapped, spin chain
compounds: the exact, low temperature value of the spin diffusivity is
computed, and compared with NMR experiments. The N=3, d=2,3 models describe
Heisenberg antiferromagnets with collinear N\'{e}el correlations, and
experimental realizations of quantum-critical behavior in these systems are
discussed. Finally, the N=2, d=2 model describes the superfluid-insulator
transition in lattice boson systems: the frequency and temperature dependence
of the the conductivity at the quantum-critical coupling is described and
implications for experiments in two-dimensional thin films and inversion layers
are noted.Comment: Lectures presented at the NATO Advanced Study Institute on "Dynamical
properties of unconventional magnetic systems", Geilo, Norway, April 2-12,
1997, edited by A. Skjeltorp and D. Sherrington, Kluwer Academic, to be
published. 46 page
Entropic Tension in Crowded Membranes
Unlike their model membrane counterparts, biological membranes are richly
decorated with a heterogeneous assembly of membrane proteins. These proteins
are so tightly packed that their excluded area interactions can alter the free
energy landscape controlling the conformational transitions suffered by such
proteins. For membrane channels, this effect can alter the critical membrane
tension at which they undergo a transition from a closed to an open state, and
therefore influence protein function \emph{in vivo}. Despite their obvious
importance, crowding phenomena in membranes are much less well studied than in
the cytoplasm.
Using statistical mechanics results for hard disk liquids, we show that
crowding induces an entropic tension in the membrane, which influences
transitions that alter the projected area and circumference of a membrane
protein. As a specific case study in this effect, we consider the impact of
crowding on the gating properties of bacterial mechanosensitive membrane
channels, which are thought to confer osmoprotection when these cells are
subjected to osmotic shock. We find that crowding can alter the gating energies
by more than in physiological conditions, a substantial fraction of
the total gating energies in some cases.
Given the ubiquity of membrane crowding, the nonspecific nature of excluded
volume interactions, and the fact that the function of many membrane proteins
involve significant conformational changes, this specific case study highlights
a general aspect in the function of membrane proteins.Comment: 20 pages (inclduing supporting information), 4 figures, to appear in
PLoS Comp. Bio
Fluctuations in granular gases
A driven granular material, e.g. a vibrated box full of sand, is a stationary
system which may be very far from equilibrium. The standard equilibrium
statistical mechanics is therefore inadequate to describe fluctuations in such
a system. Here we present numerical and analytical results concerning energy
and injected power fluctuations. In the first part we explain how the study of
the probability density function (pdf) of the fluctuations of total energy is
related to the characterization of velocity correlations. Two different regimes
are addressed: the gas driven at the boundaries and the homogeneously driven
gas. In a granular gas, due to non-Gaussianity of the velocity pdf or lack of
homogeneity in hydrodynamics profiles, even in the absence of velocity
correlations, the fluctuations of total energy are non-trivial and may lead to
erroneous conclusions about the role of correlations. In the second part of the
chapter we take into consideration the fluctuations of injected power in driven
granular gas models. Recently, real and numerical experiments have been
interpreted as evidence that the fluctuations of power injection seem to
satisfy the Gallavotti-Cohen Fluctuation Relation. We will discuss an
alternative interpretation of such results which invalidates the
Gallavotti-Cohen symmetry. Moreover, starting from the Liouville equation and
using techniques from large deviation theory, the general validity of a
Fluctuation Relation for power injection in driven granular gases is
questioned. Finally a functional is defined using the Lebowitz-Spohn approach
for Markov processes applied to the linear inelastic Boltzmann equation
relevant to describe the motion of a tracer particle. Such a functional results
to be different from injected power and to satisfy a Fluctuation Relation.Comment: 40 pages, 18 figure
Unified regression model of binding equilibria in crowded environments
Molecular crowding is a critical feature distinguishing intracellular environments
from idealized solution-based environments and is essential to understanding
numerous biochemical reactions, from protein folding to signal transduction. Many
biochemical reactions are dramatically altered by crowding, yet it is extremely
difficult to predict how crowding will quantitatively affect any particular reaction
systems. We previously developed a novel stochastic off-lattice model to efficiently
simulate binding reactions across wide parameter ranges in various crowded
conditions. We now show that a polynomial regression model can incorporate several
interrelated parameters influencing chemistry under crowded conditions. The unified
model of binding equilibria accurately reproduces the results of particle
simulations over a broad range of variation of six physical parameters that
collectively yield a complicated, non-linear crowding effect. The work represents an
important step toward the long-term goal of computationally tractable predictive
models of reaction chemistry in the cellular environment
- …