10,616 research outputs found
Above and Beyond the Landauer Bound: Thermodynamics of Modularity
Information processing typically occurs via the composition of modular units,
such as universal logic gates. The benefit of modular information processing,
in contrast to globally integrated information processing, is that complex
global computations are more easily and flexibly implemented via a series of
simpler, localized information processing operations which only control and
change local degrees of freedom. We show that, despite these benefits, there
are unavoidable thermodynamic costs to modularity---costs that arise directly
from the operation of localized processing and that go beyond Landauer's
dissipation bound for erasing information. Integrated computations can achieve
Landauer's bound, however, when they globally coordinate the control of all of
an information reservoir's degrees of freedom. Unfortunately, global
correlations among the information-bearing degrees of freedom are easily lost
by modular implementations. This is costly since such correlations are a
thermodynamic fuel. We quantify the minimum irretrievable dissipation of
modular computations in terms of the difference between the change in global
nonequilibrium free energy, which captures these global correlations, and the
local (marginal) change in nonequilibrium free energy, which bounds modular
work production. This modularity dissipation is proportional to the amount of
additional work required to perform the computational task modularly. It has
immediate consequences for physically embedded transducers, known as
information ratchets. We show how to circumvent modularity dissipation by
designing internal ratchet states that capture the global correlations and
patterns in the ratchet's information reservoir. Designed in this way,
information ratchets match the optimum thermodynamic efficiency of globally
integrated computations.Comment: 17 pages, 9 figures;
http://csc.ucdavis.edu/~cmg/compmech/pubs/idolip.ht
Stochastic Resonance in Ion Channels Characterized by Information Theory
We identify a unifying measure for stochastic resonance (SR) in voltage
dependent ion channels which comprises periodic (conventional), aperiodic and
nonstationary SR. Within a simplest setting, the gating dynamics is governed by
two-state conductance fluctuations, which switch at random time points between
two values. The corresponding continuous time point process is analyzed by
virtue of information theory. In pursuing this goal we evaluate for our
dynamics the tau-information, the mutual information and the rate of
information gain. As a main result we find an analytical formula for the rate
of information gain that solely involves the probability of the two channel
states and their noise averaged rates. For small voltage signals it simplifies
to a handy expression. Our findings are applied to study SR in a potassium
channel. We find that SR occurs only when the closed state is predominantly
dwelled. Upon increasing the probability for the open channel state the
application of an extra dose of noise monotonically deteriorates the rate of
information gain, i.e., no SR behavior occurs.Comment: 10 pages, 2 figures, to appear in Phys. Rev.
Capacity of SIMO and MISO Phase-Noise Channels with Common/Separate Oscillators
In multiple antenna systems, phase noise due to instabilities of the
radio-frequency (RF) oscillators, acts differently depending on whether the RF
circuitries connected to each antenna are driven by separate (independent)
local oscillators (SLO) or by a common local oscillator (CLO). In this paper,
we investigate the high-SNR capacity of single-input multiple-output (SIMO) and
multiple-output single-input (MISO) phase-noise channels for both the CLO and
the SLO configurations.
Our results show that the first-order term in the high-SNR capacity expansion
is the same for all scenarios (SIMO/MISO and SLO/CLO), and equal to , where stands for the SNR. On the contrary, the second-order
term, which we refer to as phase-noise number, turns out to be
scenario-dependent. For the SIMO case, the SLO configuration provides a
diversity gain, resulting in a larger phase-noise number than for the CLO
configuration. For the case of Wiener phase noise, a diversity gain of at least
can be achieved, where is the number of receive antennas. For
the MISO, the CLO configuration yields a higher phase-noise number than the SLO
configuration. This is because with the CLO configuration one can obtain a
coherent-combining gain through maximum ratio transmission (a.k.a. conjugate
beamforming). This gain is unattainable with the SLO configuration.Comment: IEEE Transactions on Communication
Dynamical decoupling efficiency versus quantum non-Markovianity
We investigate the relationship between non-Markovianity and the
effectiveness of a dynamical decoupling protocol for qubits undergoing pure
dephasing. We consider an exact model in which dephasing arises due to a
bosonic environment with a spectral density of the Ohmic class. This is
parametrised by an Ohmicity parameter by changing which we can model both
Markovian and non-Markovian environments. Interestingly, we find that
engineering a non-Markovian environment is detrimental to the efficiency of the
dynamical decoupling scheme, leading to a worse coherence preservation. We show
that each dynamical decoupling pulse reverses the flow of quantum information
and, on this basis, we investigate the connection between dynamical decoupling
efficiency and the reservoir spectral density. Finally, in the spirit of
reservoir engineering, we investigate the optimum system-reservoir parameters
for achieving maximum stationary coherences.Comment: 6 pages, 4 figure
Symmetries of the ratchet current
Recent advances in nonequilibrium statistical mechanics shed new light on the
ratchet effect. The ratchet motion can thus be understood in terms of symmetry
(breaking) considerations. We introduce an additional symmetry operation
besides time-reversal, that effectively reverses the nonequilibrium driving.
That operation of field-reversal combined with time-reversal decomposes the
nonequilibrium action so to clarify under what circumstances the ratchet
current is a second order effect around equilibrium, what is the direction of
the ratchet current and what are possibly the symmetries in its fluctuations.Comment: 13 pages, heavily extended versio
Mutual Information and Minimum Mean-square Error in Gaussian Channels
This paper deals with arbitrarily distributed finite-power input signals
observed through an additive Gaussian noise channel. It shows a new formula
that connects the input-output mutual information and the minimum mean-square
error (MMSE) achievable by optimal estimation of the input given the output.
That is, the derivative of the mutual information (nats) with respect to the
signal-to-noise ratio (SNR) is equal to half the MMSE, regardless of the input
statistics. This relationship holds for both scalar and vector signals, as well
as for discrete-time and continuous-time noncausal MMSE estimation. This
fundamental information-theoretic result has an unexpected consequence in
continuous-time nonlinear estimation: For any input signal with finite power,
the causal filtering MMSE achieved at SNR is equal to the average value of the
noncausal smoothing MMSE achieved with a channel whose signal-to-noise ratio is
chosen uniformly distributed between 0 and SNR
- …