415 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
An autonomous and reversible Maxwell's demon
Building on a model introduced by Mandal and Jarzynski [Proc. Natl. Acad.
Sci. U. S. A., {\bf 109}, (2012) 11641], we present a simple version of an
autonomous reversible Maxwell's demon. By changing the entropy of a tape
consisting of a sequence of bits passing through the demon, the demon can lift
a mass using the coupling to a heat bath. Our model becomes reversible by
allowing the tape to move in both directions. In this thermodynamically
consistent model, total entropy production consists of three terms one of which
recovers the irreversible limit studied by MJ. Our demon allows an
interpretation in terms of an enzyme transporting and transforming molecules
between compartments. Moreover, both genuine equilibrium and a linear response
regime with corresponding Onsager coefficients are well defined. Efficiency and
efficiency at maximum power are calculated. In linear response, the latter is
shown to be bounded by 1/2 if the demon operates as a machine and by 1/3 if it
is operated as an eraser.Comment: 6 pages, 3 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
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