49 research outputs found
Thermodynamic cost of external control
Artificial molecular machines are often driven by the periodic variation of
an external parameter. This external control exerts work on the system of which
a part can be extracted as output if the system runs against an applied load.
Usually, the thermodynamic cost of the process that generates the external
control is ignored. Here, we derive a refined second law for such small
machines that include this cost, which is, for example, generated by free
energy consumption of a chemical reaction that modifies the energy landscape
for such a machine. In the limit of irreversible control, this refined second
law becomes the standard one. Beyond this ideal limiting case, our analysis
shows that due to a new entropic term unexpected regimes can occur: The control
work can be smaller than the extracted work and the work required to generate
the control can be smaller than this control work. Our general inequalities are
illustrated by a paradigmatic three-state system.Comment: 11 pages, 3 figure
Coherence of Biochemical Oscillations is Bounded by Driving Force and Network Topology
Biochemical oscillations are prevalent in living organisms. Systems with a
small number of constituents cannot sustain coherent oscillations for an
indefinite time because of fluctuations in the period of oscillation. We show
that the number of coherent oscillations that quantifies the precision of the
oscillator is universally bounded by the thermodynamic force that drives the
system out of equilibrium and by the topology of the underlying biochemical
network of states. Our results are valid for arbitrary Markov processes, which
are commonly used to model biochemical reactions. We apply our results to a
model for a single KaiC protein and to an activator-inhibitor model that
consists of several molecules. From a mathematical perspective, based on strong
numerical evidence, we conjecture a universal constraint relating the imaginary
and real parts of the first non-trivial eigenvalue of a stochastic matrix.Comment: 12 pages, 13 figure
Dispersion of the time spent in a state: General expression for unicyclic model and dissipation-less precision
We compare the relation between dispersion and dissipation for two random
variables that can be used to characterize the precision of a Brownian clock.
The first random variable is the current between states. In this case, a
certain precision requires a minimal energetic cost determined by a known
thermodynamic uncertainty relation. We introduce a second random variable that
is a certain linear combination of two random variables, each of which is the
time a stochastic trajectory spends in a state. Whereas the first moment of
this random variable is equal to the average probability current, its
dispersion is generally different from the dispersion associated with the
current. Remarkably, for this second random variable a certain precision can be
obtained with an arbitrarily low energy dissipation, in contrast to the
thermodynamic uncertainty relation for the current. As a main technical
achievement, we provide an exact expression for the dispersion related to the
time that a stochastic trajectory spends in a cluster of states for a general
unicyclic network.Comment: 17 pages, 1 figur
Skewness and Kurtosis in Statistical Kinetics
We obtain lower and upper bounds on the skewness and kurtosis associated with
the cycle completion time of unicyclic enzymatic reaction schemes. Analogous to
a well known lower bound on the randomness parameter, the lower bounds on
skewness and kurtosis are related to the number of intermediate states in the
underlying chemical reaction network. Our results demonstrate that evaluating
these higher order moments with single molecule data can lead to information
about the enzymatic scheme that is not contained in the randomness parameter.Comment: 5+3 pages, 4 figure
Sensory capacity: an information theoretical measure of the performance of a sensor
For a general sensory system following an external stochastic signal, we
introduce the sensory capacity. This quantity characterizes the performance of
a sensor: sensory capacity is maximal if the instantaneous state of the sensor
has as much information about a signal as the whole time-series of the sensor.
We show that adding a memory to the sensor increases the sensory capacity. This
increase quantifies the improvement of the sensor with the addition of the
memory. Our results are obtained with the framework of stochastic
thermodynamics of bipartite systems, which allows for the definition of an
efficiency that relates the rate with which the sensor learns about the signal
with the energy dissipated by the sensor, which is given by the thermodynamic
entropy production. We demonstrate a general tradeoff between sensory capacity
and efficiency: if the sensory capacity is equal to its maximum 1, then the
efficiency must be less than 1/2. As a physical realization of a sensor we
consider a two component cellular network estimating a fluctuating external
ligand concentration as signal. This model leads to coupled linear Langevin
equations that allow us to obtain explicit analytical results.Comment: 15 pages, 7 figure