48 research outputs found
Effective thermodynamics for a marginal observer
Thermodynamics is usually formulated on the presumption that the observer has
complete information about the system he/she deals with: no parasitic current,
exact evaluation of the forces that drive the system. For example, the
acclaimed Fluctuation Relation (FR), relating the probability of time-forward
and time-reversed trajectories, assumes that the measurable transitions suffice
to characterize the process as Markovian (in our case, a continuous-time jump
process). However, most often the observer only measures a marginal current. We
show that he/she will nonetheless produce an effective description that does
not dispense with the fundamentals of thermodynamics, including the FR and the
2nd law. Our results stand on the mathematical construction of a hidden time
reversal of the dynamics, and on the physical requirement that the observed
current only accounts for a single transition in the configuration space of the
system. We employ a simple abstract example to illustrate our results and to
discuss the feasibility of generalizations.Comment: 8 pages, 1 figur
Transient fluctuation theorems for the currents and initial equilibrium ensembles
We prove a transient fluctuation theorem for the currents for continuous-time
Markov jump processes with stationary rates, generalizing an asymptotic result
by Andrieux and Gaspard [J. Stat. Phys. 127, 107 (2007)] to finite times. The
result is based on a graph theoretical decomposition in cycle currents and an
additional set of tidal currents that characterize the transient relaxation
regime. The tidal term can then be removed by a preferred choice of a suitable
initial equilibrium ensemble, a result that provides the general theory for the
fluctuation theorem without ensemble quantities recently addressed in [Phys.
Rev. E 89, 052119 (2014)]. As an example we study the reaction network of a
simple stochastic chemical engine, and finally we digress on general properties
of fluctuation relations for more complex chemical reaction networks.Comment: 19 pages, 2 figures. Sign error corrected in Eq.(50) and followin
Dissipation in noisy chemical networks: The role of deficiency
We study the effect of intrinsic noise on the thermodynamic balance of
complex chemical networks subtending cellular metabolism and gene regulation. A
topological network property called deficiency, known to determine the
possibility of complex behavior such as multistability and oscillations, is
shown to also characterize the entropic balance. In particular, only when
deficiency is zero does the average stochastic dissipation rate equal that of
the corresponding deterministic model, where correlations are disregarded. In
fact, dissipation can be reduced by the effect of noise, as occurs in a toy
model of metabolism that we employ to illustrate our findings. This phenomenon
highlights that there is a close interplay between deficiency and the
activation of new dissipative pathways at low molecule numbers.Comment: 10 Pages, 6 figure
Efficiency statistics at all times: Carnot limit at finite power
We derive the statistics of the efficiency under the assumption that
thermodynamic fluxes fluctuate with normal law, parametrizing it in terms of
time, macroscopic efficiency, and a coupling parameter . It has a
peculiar behavior: No moments, one sub- and one super-Carnot maxima
corresponding to reverse operating regimes (engine/pump), the most probable
efficiency decreasing in time. The limit where the Carnot bound
can be saturated gives rise to two extreme situations, one where the machine
works at its macroscopic efficiency, with Carnot limit corresponding to no
entropy production, and one where for a transient time scaling like
microscopic fluctuations are enhanced in such a way that the most probable
efficiency approaches Carnot at finite entropy production.Comment: 5+4 pages, 4 figures. Title modifie
Effective fluctuation and response theory
The response of thermodynamic systems perturbed out of an equilibrium
steady-state is described by the reciprocal and the fluctuation-dissipation
relations. The so-called fluctuation theorems extended the study of
fluctuations far beyond equilibrium. All these results rely on the crucial
assumption that the observer has complete information about the system. Such a
precise control is difficult to attain, hence the following questions are
compelling: Will an observer who has marginal information be able to perform an
effective thermodynamic analysis? Given that such observer will only establish
local equilibrium amidst the whirling of hidden degrees of freedom, by
perturbing the stalling currents will he/she observe equilibrium-like
fluctuations? We model the dynamics of open systems as Markov jump processes on
finite networks. We establish that: 1) While marginal currents do not obey a
full-fledged fluctuation relation, there exist effective affinities for which
an integral fluctuation relation holds; 2) Under reasonable assumptions on the
parametrization of the rates, effective and "real" affinities only differ by a
constant; 3) At stalling, i.e. where the marginal currents vanish, a
symmetrized fluctuation-dissipation relation holds while reciprocity does not;
4) There exists a notion of marginal time-reversal that plays a role akin to
that played by time-reversal for complete systems, which restores the
fluctuation relation and reciprocity. The above results hold for
configuration-space currents, and for phenomenological currents provided that
certain symmetries of the effective affinities are respected - a condition
whose range of validity we deem the most interesting question left open to
future inquiry. Our results are constructive and operational: we provide an
explicit expression for the effective affinities and propose a procedure to
measure them in laboratory.Comment: 41 pages. Comments are welcome
Extreme value statistics of edge currents in Markov jump processes and their use for entropy production estimation
The infimum of an integrated current is its extreme value against the
direction of its average flow. Using martingale theory, we show that the infima
of integrated edge currents in time-homogeneous Markov jump processes are
geometrically distributed, with a mean value determined by the effective
affinity measured by a marginal observer that only sees the integrated edge
current. In addition, we show that a marginal observer can estimate a finite
fraction of the average entropy production rate in the underlying
nonequilibrium process from the extreme value statistics in the integrated edge
current. The estimated average rate of dissipation obtained in this way equals
the above mentioned effective affinity times the average edge current.
Moreover, we show that estimates of dissipation based on extreme value
statistics can be significantly more accurate than those based on thermodynamic
uncertainty ratios, as well as those based on a naive estimator obtained by
neglecting nonMarkovian correlations in the Kullback-Leibler divergence of the
trajectories of the integrated edge current.Comment: 38 pages, 6 figure