1,304 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
Tightening the uncertainty principle for stochastic currents
We connect two recent advances in the stochastic analysis of nonequilibrium
systems: the (loose) uncertainty principle for the currents, which states that
statistical errors are bounded by thermodynamic dissipation; and the analysis
of thermodynamic consistency of the currents in the light of symmetries.
Employing the large deviation techniques presented in [Gingrich et al., Phys.
Rev. Lett. 2016] and [Pietzonka et al., Phys. Rev. E 2016], we provide a short
proof of the loose uncertainty principle, and prove a tighter uncertainty
relation for a class of thermodynamically consistent currents . Our bound
involves a measure of partial entropy production, that we interpret as the
least amount of entropy that a system sustaining current can possibly
produce, at a given steady state. We provide a complete mathematical discussion
of quadratic bounds which allows to determine which are optimal, and finally we
argue that the relationship for the Fano factor of the entropy production rate
is the most significant
realization of the loose bound. We base our analysis both on the formalism of
diffusions, and of Markov jump processes in the light of Schnakenberg's cycle
analysis.Comment: 13 pages, 4 figure
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
Multicyclic Norias: A First-Transition Approach to Extreme Values of the Currents
For continuous-time Markov chains we prove that, depending on the notion of effective affinity F, the probability of an edge current to ever become negative is either 1 if F<0 else ∼exp-F. The result generalizes a “noria” formula to multicyclic networks. We give operational insights on the effective affinity and compare several estimators, arguing that stopping problems may be more accurate in assessing the nonequilibrium nature of a system according to a local observer. Finally we elaborate on the similarity with the Boltzmann formula. The results are based on a constructive first-transition approach.</p
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