560 research outputs found
Entropy and Its Quantum Thermodynamical Implication for Anomalous Spectral Systems
The state function entropy and its quantum thermodynamical implication for
two typical dissipative systems with anomalous spectral densities are studied
by investigating on their low-temperature quantum behavior. In all cases it is
found that the entropy decays quickly and vanishes as the temperature
approaches zero. This reveals a good conformity with the third law of
thermodynamics and provides another evidence for the validity of fundamental
thermodynamical laws in the quantum dissipative region.Comment: 10 pages, 3 figure
Stochastic equation for a jumping process with long-time correlations
A jumping process, defined in terms of jump size distribution and waiting
time distribution, is presented. The jumping rate depends on the process value.
The process, which is Markovian and stationary, relaxes to an equilibrium and
is characterized by the power-law autocorrelation function. Therefore, it can
serve as a model of the 1/f noise as well as a model of the stochastic force in
the generalized Langevin equation. This equation is solved for the noise
correlations 1/t; the resulting velocity distribution has sharply falling
tails. The system preserves the memory about the initial condition for a very
long time.Comment: 7 pages, 5 Postscript figure
Specific heat anomalies of open quantum systems
The evaluation of the specific heat of an open, damped quantum system is a
subtle issue. One possible route is based on the thermodynamic partition
function which is the ratio of the partition functions of system plus bath and
of the bath alone. For the free damped particle it has been shown, however,
that the ensuing specific heat may become negative for appropriately chosen
environments. Being an open system this quantity then naturally must be
interpreted as the change of the specific heat obtained as the difference
between the specific heat of the heat bath coupled to the system degrees of
freedom and the specific heat of the bath alone. While this difference may
become negative, the involved specific heats themselves are always positive;
thus, the known thermodynamic stability criteria are perfectly guaranteed. For
a damped quantum harmonic oscillator, instead of negative values, under
appropriate conditions one can observe a dip in the difference of specific
heats as a function of temperature. Stylized minimal models containing a single
oscillator heat bath are employed to elucidate the occurrence of the anomalous
temperature dependence of the corresponding specific heat values. Moreover, we
comment on the consequences for the interpretation of the density of states
based on the thermal partitionfunction.Comment: 7 pages, 6 figures, new title and some modifications of the main tex
Relativistic Brownian motion: From a microscopic binary collision model to the Langevin equation
The Langevin equation (LE) for the one-dimensional relativistic Brownian
motion is derived from a microscopic collision model. The model assumes that a
heavy point-like Brownian particle interacts with the lighter heat bath
particles via elastic hard-core collisions. First, the commonly known,
non-relativistic LE is deduced from this model, by taking into account the
non-relativistic conservation laws for momentum and kinetic energy.
Subsequently, this procedure is generalized to the relativistic case. There, it
is found that the relativistic stochastic force is still \gd-correlated
(white noise) but does \emph{no} longer correspond to a Gaussian white noise
process. Explicit results for the friction and momentum-space diffusion
coefficients are presented and discussed.Comment: v2: Eqs. (17c) and (28) corrected; v3: discussion extended, Eqs. (33)
added, thereby connection to earlier work clarified; v4: final version,
accepted for publication in Phys. Rev.
Anomalous diffusion for overdamped particles driven by cross-correlated white noise sources
We study the statistical properties of overdamped particles driven by two
cross-correlated multiplicative Gaussian white noises in a time-dependent
environment. Using the Langevin and Fokker-Planck approaches, we derive the
exact probability distribution function for the particle positions, calculate
its moments and find their corresponding long-time, asymptotic behaviors. The
generally anomalous diffusive regimes of the particles are classified, and
their dependence on the friction coefficient and the characteristics of the
noises is analyzed in detail. The asymptotic predictions are confirmed by exact
solutions for two examples.Comment: 15 page
Capacitance fluctuations causing channel noise reduction in stochastic Hodgkin-Huxley systems
Voltage-dependent ion channels determine the electric properties of axonal
cell membranes. They not only allow the passage of ions through the cell
membrane but also contribute to an additional charging of the cell membrane
resulting in the so-called capacitance loading. The switching of the channel
gates between an open and a closed configuration is intrinsically related to
the movement of gating charge within the cell membrane. At the beginning of an
action potential the transient gating current is opposite to the direction of
the current of sodium ions through the membrane. Therefore, the excitability is
expected to become reduced due to the influence of a gating current. Our
stochastic Hodgkin-Huxley like modeling takes into account both the channel
noise -- i.e. the fluctuations of the number of open ion channels -- and the
capacitance fluctuations that result from the dynamics of the gating charge. We
investigate the spiking dynamics of membrane patches of variable size and
analyze the statistics of the spontaneous spiking. As a main result, we find
that the gating currents yield a drastic reduction of the spontaneous spiking
rate for sufficiently large ion channel clusters. Consequently, this
demonstrates a prominent mechanism for channel noise reduction.Comment: 18 page
Ratcheting Heat Flux against a Thermal Bias
Merely rocking the temperature in one heat bath can direct a steady heat flux
from cold to hot against a non-zero thermal bias in stylized nonlinear lattice
junctions that are sandwiched between two heat baths. Likewise, for an average
zero-temperature difference between the two contacts a net, ratchet-like heat
flux emerges. Computer simulations show that this very heat flux can be
controlled and reversed by suitably tailoring the frequency ( 100
MHz) of the alternating temperature field.Comment: 5 pages, 6 figure
Microcanonical quantum fluctuation theorems
Previously derived expressions for the characteristic function of work
performed on a quantum system by a classical external force are generalized to
arbitrary initial states of the considered system and to Hamiltonians with
degenerate spectra. In the particular case of microcanonical initial states
explicit expressions for the characteristic function and the corresponding
probability density of work are formulated. Their classical limit as well as
their relations to the respective canonical expressions are discussed. A
fluctuation theorem is derived that expresses the ratio of probabilities of
work for a process and its time reversal to the ratio of densities of states of
the microcanonical equilibrium systems with corresponding initial and final
Hamiltonians.From this Crooks-type fluctuation theorem a relation between
entropies of different systems can be derived which does not involve the time
reversed process. This entropy-from-work theorem provides an experimentally
accessible way to measure entropies.Comment: revised and extended versio
Effect of channel block on the spiking activity of excitable membranes in a stochastic Hodgkin-Huxley model
The influence of intrinsic channel noise on the spontaneous spiking activity
of poisoned excitable membrane patches is studied by use of a stochastic
generalization of the Hodgkin-Huxley model. Internal noise stemming from the
stochastic dynamics of individual ion channels is known to affect the
collective properties of the whole ion channel cluster. For example, there
exists an optimal size of the membrane patch for which the internal noise alone
causes a regular spontaneous generation of action potentials. In addition to
varying the size of ion channel clusters, living organisms may adapt the
densities of ion channels in order to optimally regulate the spontaneous
spiking activity. The influence of channel block on the excitability of a
membrane patch of certain size is twofold: First, a variation of ion channel
densities primarily yields a change of the conductance level. Second, a
down-regulation of working ion channels always increases the channel noise.
While the former effect dominates in the case of sodium channel block resulting
in a reduced spiking activity, the latter enhances the generation of
spontaneous action potentials in the case of a tailored potassium channel
blocking. Moreover, by blocking some portion of either potassium or sodium ion
channels, it is possible to either increase or to decrease the regularity of
the spike train.Comment: 10 pages, 3 figures, published 200
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