24,279 research outputs found
The Einstein-Boltzmann Relation for Thermodynamic and Hydrodynamic Fluctuations
When making the connection between the thermodynamics of irreversible
processes and the theory of stochastic processes through the
fluctuation-dissipation theorem, it is necessary to invoke a postulate of the
Einstein-Boltzmann type. For convective processes hydrodynamic fluctuations
must be included, the velocity is a dynamical variable and although the entropy
cannot depend directly on the velocity, will depend on velocity
variations. Some authors do not include velocity variations in ,
and so have to introduce a non-thermodynamic function which replaces the
entropy and does depend on the velocity. At first sight, it seems that the
introduction of such a function requires a generalisation of the
Einstein-Boltzmann relation to be invoked. We review the reason why it is not
necessary to introduce such a function, and therefore why there is no need to
generalise the Einstein-Boltzmann relation in this way. We then obtain the
fluctuation-dissipation theorem which shows some differences as compared with
the non-convective case. We also show that is a Liapunov
function when it includes velocity fluctuations.Comment: 13 Page
New tests and applications of the worldline path integral in the first order formalism
We present different non-perturbative calculations within the context of
Migdal's representation for the propagator and effective action of quantum
particles. We first calculate the exact propagators and effective actions for
Dirac, scalar and Proca fields in the presence of constant electromagnetic
fields, for an even-dimensional spacetime. Then we derive the propagator for a
charged scalar field in a spacelike vortex (i.e., instanton) background, in a
long-distance expansion, and the exact propagator for a massless Dirac field in
1+1 dimensions in an arbitrary background. Finally, we present an
interpretation of the chiral anomaly in the present context, finding a
condition that the paths must fulfil in order to have a non-vanishing anomaly.Comment: 26 page
Dynamical phase coexistence: A simple solution to the "savanna problem"
We introduce the concept of 'dynamical phase coexistence' to provide a simple
solution for a long-standing problem in theoretical ecology, the so-called
"savanna problem". The challenge is to understand why in savanna ecosystems
trees and grasses coexist in a robust way with large spatio-temporal
variability. We propose a simple model, a variant of the Contact Process (CP),
which includes two key extra features: varying external
(environmental/rainfall) conditions and tree age. The system fluctuates locally
between a woodland and a grassland phase, corresponding to the active and
absorbing phases of the underlying pure contact process. This leads to a highly
variable stable phase characterized by patches of the woodland and grassland
phases coexisting dynamically. We show that the mean time to tree extinction
under this model increases as a power-law of system size and can be of the
order of 10,000,000 years in even moderately sized savannas. Finally, we
demonstrate that while local interactions among trees may influence tree
spatial distribution and the order of the transition between woodland and
grassland phases, they do not affect dynamical coexistence. We expect dynamical
coexistence to be relevant in other contexts in physics, biology or the social
sciences.Comment: 8 pages, 7 figures. Accepted for publication in Journal of
Theoretical Biolog
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