Fluctuation-Dissipation Relations Far from Equilibrium

The response of thermodynamic systems slightly perturbed out of an equilibrium steady-state is described by two milestones of early nonequilibrium statistical mechanics: the reciprocal and the fluctuation-dissipation relations. At the turn of this century, 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: there is no hidden leakage to the environment, and every process is assigned its due thermodynamic cost. 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 be able to establish local equilibrium amidst the whirling of hidden degrees of freedom, by perturbing the stalling currents will he/she observe equilibrium-like fluctuations nevertheless? We address these two fundamental problems, providing a broad theory of the statistical behavior of some out of many currents that flow across a thermodynamic system.We model the dynamics of open systems as Markov jump processes on finite networks. Configurationspace currents count the net number of transitions between pairs of configurations; conjugate forces quantify their thermodynamic cost. Phenomenological currents are linear combinations of configuration currents, and only ensue when affinities enjoy appropriate symmetries, granting thermodynamic consistency. A complete thermodynamic description is achieved when the set of currents under consideration covers all cycles in the network, otherwise the set is marginal.Within this formalism, 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; 5) The effective affinity is the putative affinity of an observer who only has marginal information about a system and formulates a minimal model accounting for his/her steady-state observations; 6) There exist fluctuation relations across different levels in the hierarchy of more and more "complete" theories. The above results hold for configurationspace currents, and for phenomenological currents provided that certain symmetries of the effective affinities are respected -a condition that we call marginal thermodynamic consistency, which is stricter thermodynamic consistency and whose range of validity we deem the most interesting question left open to future inquiry. Our results are construc...

show abstract

“…Similarly, taking the second derivative and evaluating at stalling we rederive the FDR at stalling found in Ref. [46]:…”

Section: G Response At Stallingmentioning

confidence: 99%

Effective Fluctuation and Response Theory

Polettini

Esposito

2019

J Stat Phys

Self Cite

View full text Add to dashboard Cite

show abstract

“…[34]. The generalization of the fluctuation-dissipation theorem around NESS for systems with Markovian dynamics has been achieved from different theoretical approaches [17,19,20,[127][128][129][130][131][132][133][134][135][136]. The different generalized formulations of FDR link correlation functions of the fluctuations of the observable of interest OðxÞ in the unperturbed NESS with the linear response function of OðxÞ due to a small external time-dependent perturbation around the NESS.…”

Section: Fluctuation Dissipation Relations For Nessmentioning

confidence: 99%

Experiments in Stochastic Thermodynamics: Short History and Perspectives

2017

View full text Add to dashboard Cite

We summarize in this article the experiments which have been performed to test the theoretical findings in stochastic thermodynamics such as fluctuation theorem, Jarzynski equality, stochastic entropy, out-ofequilibrium fluctuation dissipation theorem, and the generalized first and second laws. We briefly describe experiments on mechanical oscillators, colloids, biological systems, and electric circuits in which the statistical properties of out-of-equilibrium fluctuations have been measured and characterized using the abovementioned tools. We discuss the main findings and drawbacks. Special emphasis is given to the connection between information and thermodynamics. The perspectives and followup of stochastic thermodynamics in future experiments and in practical applications are also discussed.

show abstract

“…However, here we adopt a different perspective, reported in the work of B. Altaner, M. Polettini, and M. Esposito [ 14 ], in which the concept of stalling currents is introduced in the context of stochastic thermodynamics. A current that traverses a system can be nullified because of the cancellation of a set of distinct internal processes, and is then called a stalling current .…”

Section: Introductionmentioning

confidence: 99%

“…A current that traverses a system can be nullified because of the cancellation of a set of distinct internal processes, and is then called a stalling current . Under these conditions, if the perturbative force solely affects the microscopic transitions that contribute to this current, the FDT is restored [ 14 , 15 ]. In addition, we test numerically that Onsager reciprocity relations are additionally satisfied at stalling conditions.…”

Section: Introductionmentioning

confidence: 99%

Effective Equilibrium in Out-of-Equilibrium Interacting Coupled Nanoconductors

Maisel

López

2019

Entropy

View full text Add to dashboard Cite

In the present work, we study a mesoscopic system consisting of a double quantum dot in which both quantum dots or artificial atoms are electrostatically coupled. Each dot is additionally tunnel coupled to two electronic reservoirs and driven far from equilibrium by external voltage differences. Our objective is to find configurations of these biases such that the current through one of the dots vanishes. In this situation, the validity of the fluctuation–dissipation theorem and Onsager’s reciprocity relations has been established. In our analysis, we employ a master equation formalism for a minimum model of four charge states, and limit ourselves to the sequential tunneling regime. We numerically study those configurations far from equilibrium for which we obtain a stalling current. In this scenario, we explicitly verify the fluctuation–dissipation theorem, as well as Onsager’s reciprocity relations, which are originally formulated for systems in which quantum transport takes place in the linear regime.

show abstract

Fluctuation-Dissipation Relations Far from Equilibrium

Cited by 45 publications

References 50 publications

Effective Fluctuation and Response Theory

Effective Fluctuation and Response Theory

Experiments in Stochastic Thermodynamics: Short History and Perspectives

Effective Equilibrium in Out-of-Equilibrium Interacting Coupled Nanoconductors

Contact Info

Product

Resources

About