497 research outputs found
Entropy production of cyclic population dynamics
Entropy serves as a central observable in equilibrium thermodynamics.
However, many biological and ecological systems operate far from thermal
equilibrium. Here we show that entropy production can characterize the behavior
of such nonequilibrium systems. To this end we calculate the entropy production
for a population model that displays nonequilibrium behavior resulting from
cyclic competition. At a critical point the dynamics exhibits a transition from
large, limit-cycle like oscillations to small, erratic oscillations. We show
that the entropy production peaks very close to the critical point and tends to
zero upon deviating from it. We further provide analytical methods for
computing the entropy production which agree excellently with numerical
simulations.Comment: 4 pages, 3 figures and Supplementary Material. To appear in Phys.
Rev. Lett.
Inflation with a graceful exit and entrance driven by Hawking radiation
We present a model for cosmological inflation which has a natural "turn on"
and a natural "turn off" mechanism. In our model inflation is driven by the
Hawking-like radiation that occurs in Friedman-Robertson-Walker (FRW)
space-time. This Hawking-like radiation results in an effective negative
pressure "fluid" which leads to a rapid period of expansion in the very early
Universe. As the Universe expands the FRW Hawking temperature decreases and the
inflationary expansion turns off and makes a natural transition to the power
law expansion of a radiation dominated universe. The "turn on" mechanism is
more speculative, but is based on the common hypothesis that in a quantum
theory of gravity at very high temperatures/high densities Hawking radiation
will stop. Applying this speculation to the very early Universe implies that
the Hawking-like radiation of the FRW space-time will be turned off and
therefore the inflation driven by this radiation will turn off.Comment: 19 pages, 2 figures revtex, matches PRD published versio
Spot deformation and replication in the two-dimensional Belousov-Zhabotinski reaction in water-in-oil microemulsion
In the limit of large diffusivity ratio, spot-like solutions in the
two-dimensional Belousov-Zhabotinski reaction in water-in-oil microemulsion are
studied. It is shown analytically that such spots undergo an instability as the
diffusivity ratio is decreased. An instability threshold is derived. For spots
of small radius, it is shown that this instability leads to a spot splitting
into precisely two spots. For larger spots, it leads to deformation, fingering
patterns and space-filling curves. Numerical simulations are shown to be in
close agreement with the analytical predictions.Comment: To appear, PR
Critical voltage of a mesoscopic superconductor
We study the role of the quasiparticle distribution function f on the
properties of a superconducting nanowire. We employ a numerical calculation
based upon the Usadel equation. Going beyond linear response, we find a
non-thermal distribution for f caused by an applied bias voltage. We
demonstrate that the even part of f (the energy mode f_L) drives a first order
transition from the superconducting state to the normal state irrespective of
the current
Stochastic thermodynamics under coarse-graining
A general formulation of stochastic thermodynamics is presented for open
systems exchanging energy and particles with multiple reservoirs. By
introducing a partition in terms of "macrostates" (e.g. sets of "microstates"),
the consequence on the thermodynamic description of the system is studied in
detail. When microstates within macrostates rapidly thermalize, the entire
structure of the microscopic theory is recovered at the macrostate level. This
is not the case when these microstates remain out of equilibrium leading to
additional contributions to the entropy balance. Some of our results are
illustrated for a model of two coupled quantum dots.Comment: 12 pages, 3 figure
Hydrodynamical evolution near the QCD critical end point
Hydrodynamical calculations have been successful in describing global
observables in ultrarelativistic heavy ion collisions, which aim to observe the
production of the quark-gluon plasma. On the other hand, recently, a lot of
evidence that there exists a critical end point (CEP) in the QCD phase diagram
has been accumulating. Nevertheless, so far, no equation of state with the CEP
has been employed in hydrodynamical calculations. In this paper, we construct
the equation of state with the CEP on the basis of the universality hypothesis
and show that the CEP acts as an attractor of isentropic trajectories. We also
consider the time evolution in the case with the CEP and discuss how the CEP
affects the final state observables, such as the correlation length,
fluctuation, chemical freezeout, kinetic freezeout, and so on. Finally, we
argue that the anomalously low kinetic freezeout temperature at the BNL
Relativistic Heavy Ion Collider suggests the possibility of the existence of
the CEP.Comment: 13 pages, 12 figures, accepted for publication in Physical Review
Thermodynamics of Chemical Waves
Chemical waves constitute a known class of dissipative structures emerging in
reaction-diffusion systems. They play a crucial role in biology, spreading
information rapidly to synchronize and coordinate biological events. We develop
a rigorous thermodynamic theory of reaction-diffusion systems to characterize
chemical waves. Our main result is the definition of the proper thermodynamic
potential of the local dynamics as a nonequilibrium free energy density and
establishing its balance equation. This enables us to identify the dynamics of
the free energy, of the dissipation, and of the work spent to sustain the wave
propagation. Two prototypical classes of chemical waves are examined. From a
thermodynamic perspective, the first is sustained by relaxation towards
equilibrium and the second by nonconservative forces generated by chemostats.
We analytically study step-like waves, called wavefronts, using the
Fisher-Kolmogorov equation as representative of the first class and oscillating
waves in the Brusselator model as representative of the second. Given the
fundamental role of chemical waves as message carriers in biosystems, our
thermodynamic theory constitutes an important step toward an understanding of
information transfers and processing in biology.Comment: 12 pages, 2 figure
Monotone return to steady nonequilibrium
We propose and analyze a new candidate Lyapunov function for relaxation
towards general nonequilibrium steady states. The proposed functional is
obtained from the large time asymptotics of time-symmetric fluctuations. For
driven Markov jump or diffusion processes it measures an excess in dynamical
activity rates. We present numerical evidence and we report on a rigorous
argument for its monotonous time-dependence close to the steady nonequilibrium
or in general after a long enough time. This is in contrast with the behavior
of approximate Lyapunov functions based on entropy production that when driven
far from equilibrium often keep exhibiting temporal oscillations even close to
stationarity.Comment: Accepted for publication in Phys. Rev. Let
Emergent Hydrodynamics in Integrable Quantum Systems Out of Equilibrium
Understanding the general principles underlying strongly interacting quantum states out of equilibrium is one of the most important tasks of current theoretical physics. With experiments accessing the intricate dynamics of many-body quantum systems, it is paramount to develop powerful methods that encode the emergent physics. Up to now, the strong dichotomy observed between integrable and nonintegrable evolutions made an overarching theory difficult to build, especially for transport phenomena where space-time profiles are drastically different. We present a novel framework for studying transport in integrable systems: hydrodynamics with infinitely many conservation laws. This bridges the conceptual gap between integrable and nonintegrable quantum dynamics, and gives powerful tools for accurate studies of space-time profiles. We apply it to the description of energy transport between heat baths, and provide a full description of the current-carrying nonequilibrium steady state and the transition regions in a family of models including the Lieb-Liniger model of interacting Bose gases, realized in experiments
Energy and entropy of relativistic diffusing particles
We discuss energy-momentum tensor and the second law of thermodynamics for a
system of relativistic diffusing particles. We calculate the energy and entropy
flow in this system. We obtain an exact time dependence of energy, entropy and
free energy of a beam of photons in a reservoir of a fixed temperature.Comment: 14 pages,some formulas correcte
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