3,041 research outputs found
Heat release by controlled continuous-time Markov jump processes
We derive the equations governing the protocols minimizing the heat released
by a continuous-time Markov jump process on a one-dimensional countable state
space during a transition between assigned initial and final probability
distributions in a finite time horizon. In particular, we identify the
hypotheses on the transition rates under which the optimal control strategy and
the probability distribution of the Markov jump problem obey a system of
differential equations of Hamilton-Bellman-Jacobi-type. As the state-space mesh
tends to zero, these equations converge to those satisfied by the diffusion
process minimizing the heat released in the Langevin formulation of the same
problem. We also show that in full analogy with the continuum case, heat
minimization is equivalent to entropy production minimization. Thus, our
results may be interpreted as a refined version of the second law of
thermodynamics.Comment: final version, section 2.1 revised, 26 pages, 3 figure
On the efficiency of heat engines at the micro-scale and below
We investigate the thermodynamic efficiency of sub-micro-scale heat engines
operating under the conditions described by over-damped stochastic
thermodynamics. We prove that at maximum power the efficiency obeys for
constant isotropic mobility the universal law
where is the efficiency of an ideal Carnot cycle. The corresponding
power optimizing protocol is specified by the solution of an optimal mass
transport problem. Such solution can be determined explicitly using well known
Monge--Amp\`ere--Kantorovich reconstruction algorithms. Furthermore, we show
that the same law describes the efficiency of heat engines operating at maximum
work over short time periods. Finally, we illustrate the straightforward
extension of these results to cases when the mobility is anisotropic and
temperature dependent.Comment: 5 pages; revised version including the derivation of the efficiency
and of the corresponding optimal protocols in the presence of anisotropic
temperature dependent mobilit
General no-go condition for stochastic pumping
The control of chemical dynamics requires understanding the effect of
time-dependent transition rates between states of chemo-mechanical molecular
configurations. Pumping refers to generating a net current, e.g. per period in
the time-dependence, through a cycle of consecutive states. The working of
artificial machines or synthesized molecular motors depends on it. In this
paper we give short and simple proofs of no-go theorems, some of which appeared
before but here with essential extensions to non-Markovian dynamics, including
the study of the diffusion limit. It allows to exclude certain protocols in the
working of chemical motors where only the depth of the energy well is changed
in time and not the barrier height between pairs of states. We also show how
pre-existing steady state currents are in general modified with a
multiplicative factor when this time-dependence is turned on.Comment: 8 pages; v2: minor changes, 1 reference adde
The Dynamics of Internet Traffic: Self-Similarity, Self-Organization, and Complex Phenomena
The Internet is the most complex system ever created in human history.
Therefore, its dynamics and traffic unsurprisingly take on a rich variety of
complex dynamics, self-organization, and other phenomena that have been
researched for years. This paper is a review of the complex dynamics of
Internet traffic. Departing from normal treatises, we will take a view from
both the network engineering and physics perspectives showing the strengths and
weaknesses as well as insights of both. In addition, many less covered
phenomena such as traffic oscillations, large-scale effects of worm traffic,
and comparisons of the Internet and biological models will be covered.Comment: 63 pages, 7 figures, 7 tables, submitted to Advances in Complex
System
Engineered swift equilibration of a Brownian particle
A fundamental and intrinsic property of any device or natural system is its
relaxation time relax, which is the time it takes to return to equilibrium
after the sudden change of a control parameter [1]. Reducing relax , is
frequently necessary, and is often obtained by a complex feedback process. To
overcome the limitations of such an approach, alternative methods based on
driving have been recently demonstrated [2, 3], for isolated quantum and
classical systems [4--9]. Their extension to open systems in contact with a
thermostat is a stumbling block for applications. Here, we design a
protocol,named Engineered Swift Equilibration (ESE), that shortcuts
time-consuming relaxations, and we apply it to a Brownian particle trapped in
an optical potential whose properties can be controlled in time. We implement
the process experimentally, showing that it allows the system to reach
equilibrium times faster than the natural equilibration rate. We also estimate
the increase of the dissipated energy needed to get such a time reduction. The
method paves the way for applications in micro and nano devices, where the
reduction of operation time represents as substantial a challenge as
miniaturization [10]. The concepts of equilibrium and of transformations from
an equilibrium state to another, are cornerstones of thermodynamics. A textbook
illustration is provided by the expansion of a gas, starting at equilibrium and
expanding to reach a new equilibrium in a larger vessel. This operation can be
performed either very slowly by a piston, without dissipating energy into the
environment, or alternatively quickly, letting the piston freely move to reach
the new volume
Optimization of transport protocols with path-length constraints in complex networks
We propose a protocol optimization technique that is applicable to both
weighted or unweighted graphs. Our aim is to explore by how much a small
variation around the Shortest Path or Optimal Path protocols can enhance
protocol performance. Such an optimization strategy can be necessary because
even though some protocols can achieve very high traffic tolerance levels, this
is commonly done by enlarging the path-lengths, which may jeopardize
scalability. We use ideas borrowed from Extremal Optimization to guide our
algorithm, which proves to be an effective technique. Our method exploits the
degeneracy of the paths or their close-weight alternatives, which significantly
improves the scalability of the protocols in comparison to Shortest Paths or
Optimal Paths protocols, keeping at the same time almost intact the length or
weight of the paths. This characteristic ensures that the optimized routing
protocols are composed of paths that are quick to traverse, avoiding negative
effects in data communication due to path-length increases that can become
specially relevant when information losses are present.Comment: 8 pages, 8 figure
- …