48 research outputs found
Entropy and Nonlinear Nonequilibrium Thermodynamic Relation for Heat Conducting Steady States
Among various possible routes to extend entropy and thermodynamics to
nonequilibrium steady states (NESS), we take the one which is guided by
operational thermodynamics and the Clausius relation. In our previous study, we
derived the extended Clausius relation for NESS, where the heat in the original
relation is replaced by its "renormalized" counterpart called the excess heat,
and the Gibbs-Shannon expression for the entropy by a new symmetrized
Gibbs-Shannon-like expression. Here we concentrate on Markov processes
describing heat conducting systems, and develop a new method for deriving
thermodynamic relations. We first present a new simpler derivation of the
extended Clausius relation, and clarify its close relation with the linear
response theory. We then derive a new improved extended Clausius relation with
a "nonlinear nonequilibrium" contribution which is written as a correlation
between work and heat. We argue that the "nonlinear nonequilibrium"
contribution is unavoidable, and is determined uniquely once we accept the
(very natural) definition of the excess heat. Moreover it turns out that to
operationally determine the difference in the nonequilibrium entropy to the
second order in the temperature difference, one may only use the previous
Clausius relation without a nonlinear term or must use the new relation,
depending on the operation (i.e., the path in the parameter space). This
peculiar "twist" may be a clue to a better understanding of thermodynamics and
statistical mechanics of NESS.Comment: 31 pages, 4 figure
Model study on steady heat capacity in driven stochastic systems
We explore two- and three-state Markov models driven out of thermal
equilibrium by non-potential forces to demonstrate basic properties of the
steady heat capacity based on the concept of quasistatic excess heat. It is
shown that large enough driving forces can make the steady heat capacity
negative. For both the low- and high-temperature regimes we propose an
approximative thermodynamic scheme in terms of "dynamically renormalized"
effective energy levels.Comment: 10 pages, 7 figures, 1 tabl
A nonequilibrium extension of the Clausius heat theorem
We generalize the Clausius (in)equality to overdamped mesoscopic and
macroscopic diffusions in the presence of nonconservative forces. In contrast
to previous frameworks, we use a decomposition scheme for heat which is based
on an exact variant of the Minimum Entropy Production Principle as obtained
from dynamical fluctuation theory. This new extended heat theorem holds true
for arbitrary driving and does not require assumptions of local or close to
equilibrium. The argument remains exactly intact for diffusing fields where the
fields correspond to macroscopic profiles of interacting particles under
hydrodynamic fluctuations. We also show that the change of Shannon entropy is
related to the antisymmetric part under a modified time-reversal of the
time-integrated entropy flux.Comment: 23 pages; v2: manuscript significantly extende
Representation of nonequilibrium steady states in large mechanical systems
Recently a novel concise representation of the probability distribution of
heat conducting nonequilibrium steady states was derived. The representation is
valid to the second order in the ``degree of nonequilibrium'', and has a very
suggestive form where the effective Hamiltonian is determined by the excess
entropy production. Here we extend the representation to a wide class of
nonequilibrium steady states realized in classical mechanical systems where
baths (reservoirs) are also defined in terms of deterministic mechanics. The
present extension covers such nonequilibrium steady states with a heat
conduction, with particle flow (maintained either by external field or by
particle reservoirs), and under an oscillating external field. We also simplify
the derivation and discuss the corresponding representation to the full order.Comment: 27 pages, 3 figure
Extended Clausius Relation and Entropy for Nonequilibrium Steady States in Heat Conducting Quantum Systems
Recently, in their attempt to construct steady state thermodynamics (SST),
Komatsu, Nakagwa, Sasa, and Tasaki found an extension of the Clausius relation
to nonequilibrium steady states in classical stochastic processes. Here we
derive a quantum mechanical version of the extended Clausius relation. We
consider a small system of interest attached to large systems which play the
role of heat baths. By only using the genuine quantum dynamics, we realize a
heat conducting nonequilibrium steady state in the small system. We study the
response of the steady state when the parameters of the system are changed
abruptly, and show that the extended Clausius relation, in which "heat" is
replaced by the "excess heat", is valid when the temperature difference is
small. Moreover we show that the entropy that appears in the relation is
similar to von Neumann entropy but has an extra symmetrization with respect to
time-reversal. We believe that the present work opens a new possibility in the
study of nonequilibrium phenomena in quantum systems, and also confirms the
robustness of the approach by Komtatsu et al.Comment: 19 pages, 2 figure
Velocity Statistics in the Two-Dimensional Granular Turbulence
We studied the macroscopic statistical properties on the freely evolving
quasi-elastic hard disk (granular) system by performing a large-scale (up to a
few million particles) event-driven molecular dynamics systematically and found
that remarkably analogous to an enstrophy cascade process in the decaying
two-dimensional fluid turbulence. There are four typical stages in the freely
evolving inelastic hard disk system, which are homogeneous, shearing (vortex),
clustering and final state. In the shearing stage, the self-organized
macroscopic coherent vortices become dominant. In the clustering stage, the
energy spectra are close to the expectation of Kraichnan-Batchelor theory and
the squared two-particle separation strictly obeys Richardson law.Comment: 4 pages, 4 figures, to be published in PR
Breather lattice and its stabilization for the modified Korteweg-de Vries equation
We obtain an exact solution for the breather lattice solution of the modified
Korteweg-de Vries (MKdV) equation. Numerical simulation of the breather lattice
demonstrates its instability due to the breather-breather interaction. However,
such multi-breather structures can be stabilized through the concurrent
application of ac driving and viscous damping terms.Comment: 6 pages, 3 figures, Phys. Rev. E (in press
CMB constraints on noncommutative geometry during inflation
We investigate the primordial power spectrum of the density perturbations
based on the assumption that spacetime is noncommutative in the early stage of
inflation. Due to the spacetime noncommutativity, the primordial power spectrum
can lose rotational invariance. Using the k-inflation model and slow-roll
approximation, we show that the deviation from rotational invariance of the
primordial power spectrum depends on the size of noncommutative length scale
L_s but not on sound speed. We constrain the contributions from the spacetime
noncommutativity to the covariance matrix for the harmonic coefficients of the
CMB anisotropies using five-year WMAP CMB maps. We find that the upper bound
for L_s depends on the product of sound speed and slow-roll parameter.
Estimating this product using cosmological parameters from the five-year WMAP
results, the upper bound for L_s is estimated to be less than 10^{-27} cm at
99.7% confidence level.Comment: 8 pages, 1 figure, References added, Accepted for publication in EPJC
(submitted version
Macroscopic traffic models from microscopic car-following models
We present a method to derive macroscopic fluid-dynamic models from
microscopic car-following models via a coarse-graining procedure. The method is
first demonstrated for the optimal velocity model. The derived macroscopic
model consists of a conservation equation and a momentum equation, and the
latter contains a relaxation term, an anticipation term, and a diffusion term.
Properties of the resulting macroscopic model are compared with those of the
optimal velocity model through numerical simulations, and reasonable agreement
is found although there are deviations in the quantitative level. The
derivation is also extended to general car-following models.Comment: 12 pages, 4 figures; to appear in Phys. Rev.
Steady state solutions of hydrodynamic traffic models
We investigate steady state solutions of hydrodynamic traffic models in the
absence of any intrinsic inhomogeneity on roads such as on-ramps. It is shown
that typical hydrodynamic models possess seven different types of inhomogeneous
steady state solutions. The seven solutions include those that have been
reported previously only for microscopic models. The characteristic properties
of wide jam such as moving velocity of its spatiotemporal pattern and/or
out-flux from wide jam are shown to be uniquely determined and thus independent
of initial conditions of dynamic evolution. Topological considerations suggest
that all of the solutions should be common to a wide class of traffic models.
The results are discussed in connection with the universality conjecture for
traffic models. Also the prevalence of the limit-cycle solution in a recent
study of a microscopic model is explained in this approach.Comment: 9 pages, 6 figure