21 research outputs found
Foundations of Stochastic Thermodynamics
Small systems in a thermodynamic medium --- like colloids in a suspension or
the molecular machinery in living cells --- are strongly affected by the
thermal fluctuations of their environment. Physicists model such systems by
means of stochastic processes. Stochastic Thermodynamics (ST) defines entropy
changes and other thermodynamic notions for individual realizations of such
processes. It applies to situations far from equilibrium and provides a unified
approach to stochastic fluctuation relations. Its predictions have been studied
and verified experimentally.
This thesis addresses the theoretical foundations of ST. Its focus is on the
following two aspects: (i) The stochastic nature of mesoscopic observations has
its origin in the molecular chaos on the microscopic level. Can one derive ST
from an underlying reversible deterministic dynamics? Can we interpret ST's
notions of entropy and entropy changes in a well-defined
information-theoretical framework? (ii) Markovian jump processes on finite
state spaces are common models for bio-chemical pathways. How does one quantify
and calculate fluctuations of physical observables in such models? What role
does the topology of the network of states play? How can we apply our abstract
results to the design of models for molecular motors?
The thesis concludes with an outlook on dissipation as information written to
unobserved degrees of freedom --- a perspective that yields a consistency
criterion between dynamical models formulated on various levels of description.Comment: Ph.D. Thesis, G\"ottingen 2014, Keywords: Stochastic Thermodynamics,
Entropy, Dissipation, Markov processes, Large Deviation Theory, Molecular
Motors, Kinesi
Fluctuating Currents in Stochastic Thermodynamics I. Gauge Invariance of Asymptotic Statistics
Stochastic Thermodynamics uses Markovian jump processes to model random
transitions between observable mesoscopic states. Physical currents are
obtained from anti-symmetric jump observables defined on the edges of the graph
representing the network of states. The asymptotic statistics of such currents
are characterized by scaled cumulants. In the present work, we use the
algebraic and topological structure of Markovian models to prove a gauge
invariance of the scaled cumulant-generating function. Exploiting this
invariance yields an efficient algorithm for practical calculations of
asymptotic averages and correlation integrals. We discuss how our approach
generalizes the Schnakenberg decomposition of the average entropy-production
rate, and how it unifies previous work. The application of our results to
concrete models is presented in an accompanying publication.Comment: PACS numbers: 05.40.-a, 05.70.Ln, 02.50.Ga, 02.10.Ox. An accompanying
pre-print "Fluctuating Currents in Stochastic Thermodynamics II. Energy
Conversion and Nonequilibrium Response in Kinesin Models" by the same authors
is available as arXiv:1504.0364
Fluctuating Currents in Stochastic Thermodynamics II. Energy Conversion and Nonequilibrium Response in Kinesin Models
Unlike macroscopic engines, the molecular machinery of living cells is
strongly affected by fluctuations. Stochastic Thermodynamics uses Markovian
jump processes to model the random transitions between the chemical and
configurational states of these biological macromolecules. A recently developed
theoretical framework [Wachtel, Vollmer, Altaner: "Fluctuating Currents in
Stochastic Thermodynamics I. Gauge Invariance of Asymptotic Statistics"]
provides a simple algorithm for the determination of macroscopic currents and
correlation integrals of arbitrary fluctuating currents. Here, we use it to
discuss energy conversion and nonequilibrium response in different models for
the molecular motor kinesin. Methodologically, our results demonstrate the
effectiveness of the algorithm in dealing with parameter-dependent stochastic
models. For the concrete biophysical problem our results reveal two interesting
features in experimentally accessible parameter regions: The validity of a
non-equilibrium Green--Kubo relation at mechanical stalling as well as negative
differential mobility for superstalling forces.Comment: PACS numbers: 05.70.Ln, 05.40.-a, 87.10.Mn, 87.16.Nn. An accompanying
publication "Fluctuating Currents in Stochastic Thermodynamics I. Gauge
Invariance of Asymptotic Statistics" is available at
http://arxiv.org/abs/1407.206
Fluctuation preserving coarse graining for biochemical systems
Finite stochastic Markov models play a major role for modelling biochemical
pathways. Such models are a coarse-grained description of the underlying
microscopic dynamics and can be considered mesoscopic. The level of
coarse-graining is to a certain extend arbitrary since it depends on the
resolution of accomodating measurements. Here, we present a way to simplify
such stochastic descriptions, which preserves both the meso-micro and the
meso-macro connection. The former is achieved by demanding locality, the latter
by considering cycles on the network of states. Using single- and multicycle
examples we demonstrate how our new method preserves fluctuations of
observables much better than na\"ive approaches.Comment: PACS: 87.10.Mn, 05.40.-a, 05.70.Ln, 87.18.Tt (4 pages, 4 figures
Fluctuation-Dissipation Relations Far from Equilibrium
Near equilibrium, where all currents of a system vanish on average, the fluctuation-dissipation relation
(FDR) connects a current’s spontaneous fluctuations with its response to perturbations of the conjugate
thermodynamic force. Out of equilibrium, fluctuation-response relations generally involve additional
nondissipative contributions. Here, in the framework of stochastic thermodynamics, we show that an
equilibriumlike FDR holds for internally equilibrated currents, if the perturbing conjugate force only affects
the microscopic transitions that contribute to the current. We discuss the physical requirements for the
validity of our result and apply it to nanosized electronic devices