492 research outputs found
Complex heat capacity and entropy production of temperature modulated systems
Non-equilibrium systems under temperature modulation are investigated in the
light of the stochastic thermodynamics. We show that, for small amplitudes of
the temperature oscillations, the heat flux behaves sinusoidally with time, a
result that allows the definition of the complex heat capacity. The real part
of the complex heat capacity is the dynamic heat capacity, and its imaginary
part is shown to be proportional to the rate of entropy production. We also
show that the poles of the complex heat capacity are equal to imaginary unit
multiplied by the eigenvalues of the unperturbed evolution operator, and are
all located in the lower half plane of the complex frequency, assuring that the
Kramers-Kronig relations are obeyed. We have also carried out an exact
calculation of the complex heat capacity of a harmonic solid and determined the
dispersion relation of the dynamic heat capacity and of the rate of entropy
production
Stochastic approach to equilibrium and nonequilibrium thermodynamics
We develop the stochastic approach to thermodynamics based on the stochastic
dynamics, which can be discrete (master equation) continuous (Fokker-Planck
equation), and on two assumptions concerning entropy. The first is the
definition of entropy itself and the second, the definition of entropy
production rate which is nonnegative and vanishes in thermodynamic equilibrium.
Based on these assumptions we study interacting systems with many degrees of
freedom in equilibrium or out of thermodynamic equilibrium, and how the
macroscopic laws are derived from the stochastic dynamics. These studies
include the quasi-equilibrium processes, the convexity of the equilibrium
surface, the monotonic time behavior of thermodynamic potentials, including
entropy, the bilinear form of the entropy production rate, the Onsager
coefficients and reciprocal relations, and the nonequilibrium steady states of
chemical reactions
Stationary Coverage of a Stochastic Adsorption-Desorption Process with Diffusional Relaxation
We show that it is possible to derive the stationary coverage of an
adsorption-desorption process of dimers with diffusional relaxation with a very
simple ansatz for the stationary distribution of the process supplemented by a
hypothesis of global balance. Our approach is contrasted to the exact result
and we seek to understand its validity within an instance of the model.Comment: LaTeX 2.09, 7 pages, no figures, uses 'amssymb
Entropy production and heat capacity of systems under time-dependent oscillating temperature
Using the stochastic thermodynamics, we determine the entropy production and
the dynamic heat capacity of systems subject to a sinusoidally time dependent
temperature, in which case the systems are permanently out of thermodynamic
equilibrium inducing a continuous generation of entropy. The systems evolve in
time according to a Fokker-Planck or to a Fokker-Planck-Kramers equation.
Solutions of these equations, for the case of harmonic forces, are found
exactly from which the heat flux, the production of entropy and the dynamic
heat capacity are obtained as functions of the frequency of the temperature
modulation. These last two quantities are shown to be related to the real an
imaginary parts of the complex heat capacity.Comment: 7 pages, 4 figure
Type-dependent irreversible stochastic spin models for genetic regulatory networks at the level of promotion-inhibition circuitry
We describe an approach to model genetic regulatory networks at the level of
promotion-inhibition circuitry through a class of stochastic spin models that
includes spatial and temporal density fluctuations in a natural way. The
formalism can be viewed as an agent-based model formalism with agent behavior
ruled by a classical spin-like pseudo-Hamiltonian playing the role of a local,
individual objective function. A particular but otherwise generally applicable
choice for the microscopic transition rates of the models also makes them of
independent interest. To illustrate the formalism, we investigate (by Monte
Carlo simulations) some stationary state properties of the repressilator, a
synthetic three-gene network of transcriptional regulators that possesses
oscillatory behavior.Comment: 20 pages, 4 figures, 50 references. Significantly revised and updated
version accepted for publication in Physica
Subcritical series expansions for multiple-creation nonequilibrium models
Perturbative subcritical series expansions for the steady properties of a
class of one-dimensional nonequilibrium models characterized by
multiple-reaction rules are presented here. We developed long series expansions
for three nonequilibrium models: the pair-creation contact process, the
A-pair-creation contact process, which is closely related system to the
previous model, and the triplet-creation contact process. The long series
allowed us to obtain accurate estimates for the critical point and critical
exponents. Numerical simulations are also performed and compared with the
series expansions results.Comment: 14 pages and 4 figures. submited to Physical Review
Robustness of first-order phase transitions in one-dimensional long-range contact processes
It has been proposed (Phys. Rev. E {\bf 71}, 026121 (2005)) that unlike the
short range contact process, a long-range counterpart may lead to the existence
a discontinuous phase transition in one dimension. Aiming at exploring such
link, here we investigate thoroughly a family of long-range contact processes.
They are introduced through the transition rate , where
is the length of inactive islands surrounding particles. In the former
approach we reconsider the original model (called contact process), by
considering distinct mechanisms of weakening the long-range interaction toward
the short-range limit. Second, we study the effect of different rules,
including creation and annihilation by clusters of particles and distinct
versions with infinitely many absorbing states. Our results show that all
examples presenting a single absorbing state, a discontinuous transition is
possible for small . On the other hand, the presence of infinite
absorbing states leads to distinct scenario depending on the interactions at
the frontier of inactive sites
Critical properties of the contact process with quenched dilution
We have studied the critical properties of the contact process on a square
lattice with quenched site dilution by Monte Carlo simulations. This was
achieved by generating in advance the percolating cluster, through the use of
an appropriate epidemic model, and then by the simulation of the contact
process on the top of the percolating cluster. The dynamic critical exponents
were calculated by assuming an activated scaling relation and the static
exponents by the usual power law behavior. Our results are in agreement with
the prediction that the quenched diluted contact process belongs to the
universality class of the random transverse-field Ising model. We have also
analyzed the model and determined the phase diagram by the use of a mean-field
theory that takes into account the correlation between neighboring sites.Comment: 14 pages and 8 figure
Stochastic thermodynamics of system with continuous space of states
We analyze the stochastic thermodynamics of systems with continuous space of
states. The evolution equation, the rate of entropy production, and other
results are obtained by a continuous time limit of a discrete time formulation.
We point out the role of time reversal and of the dissipation part of the
probability current on the production of entropy. We show that the rate of
entropy production is a bilinear form in the components of the dissipation
probability current with coefficients being the components of the precision
matrix related to the Gaussian noise. We have also analyzed a type of noise
that makes the energy function to be strictly constant along the stochastic
trajectory, being appropriate to describe an isolated system. This type of
noise leads to nonzero entropy production and thus to an increase of entropy in
the system. This result contrasts with the invariance of the entropy predicted
by the Liouville equation, which also describes an isolated system
Positive heat capacity in the microcanonical ensemble
The positivity of the heat capacity is the hallmark of thermal stability of
systems in thermodynamic equilibrium. We show that this property remains valid
for systems with negative derivative of energy with respect to temperature, as
happens to some system described by the microcanonical ensemble. The
demonstration rests on considering a trajectory on the Gibbs equilibrium
surface, and its projection on the entropy-energy plane. The Gibbs equilibrium
surface has the convexity property, but the projection might lack this
property, leading to a negative derivative of energy with respect to
temperature
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