Microreversibility, nonequilibrium current fluctuations, and response theory

Barbier, Maximilien; Gaspard, Pierre

doi:10.1088/1751-8121/aad025

Cited by 22 publications

(77 citation statements)

References 52 publications

(278 reference statements)

Supporting

Mentioning

Contrasting

Order By: Relevance

“…We have also shown that, as a corollary of the fluctuation theorem for the currents, nonlinear transport generalizations of the fluctuation-dissipation and Onsager reciprocal relations are satisfied in the transistor. In particular, we have verified in detail that the second-order nonlinear response coefficients of the currents are related to the first-order responses of the diffusivities, as predicted by theory [11,12,14].…”

Section: Discussionsupporting

confidence: 66%

Microreversibility, fluctuations, and nonlinear transport in transistors

Gaspard

2019

Phys. Rev. E

View full text Add to dashboard Cite

We present a stochastic approach for charge transport in transistors. In this approach, the electron and hole densities are governed by diffusion-reaction stochastic differential equations satisfying local detailed balance and the electric field is determined with the Poisson equation. The approach is consistent with the laws of electricity, thermodynamics, and microreversibility. In this way, the signal amplifying effect of transistors is verified under their working conditions. We also perform the full counting statistics of the two electric currents coupled together in transistors and we show that the fluctuation theorem holds for their joint probability distribution. Similar results are obtained including the displacement currents. In addition, the Onsager reciprocal relations and their generalizations to nonlinear transport properties deduced from the fluctuation theorem are numerically shown to be satisfied. arXiv:1812.09228v1 [cond-mat.stat-mech]

show abstract

Section: Discussionsupporting

confidence: 66%

Microreversibility, fluctuations, and nonlinear transport in transistors

Gaspard

2019

Phys. Rev. E

View full text Add to dashboard Cite

show abstract

“…A surprising aspect of our recent works [33,34] has been the use of Euler's polynomials within our mathematical analysis of a fluctuation relation of the form (1), both in the absence [33] and the presence [34] of a magnetic field. In particular, we showed in [34] that the fluctuation relation constrains about half of the (symmetric and antisymmetric parts of the) cumulants and their responses to the affinities.…”

Section: Resultsmentioning

confidence: 99%

Microreversibility, nonequilibrium response, and Euler’s polynomials

Barbier¹,

Gaspard²

2020

J. Phys. A: Math. Theor.

Self Cite

View full text Add to dashboard Cite

Microreversibility constrains the fluctuations of the nonequilibrium currents that cross an open system. This can be seen from the so-called fluctuation relations, which are a direct consequence of microreversibility. Indeed, the latter are known to impose time-reversal symmetry relations on the statistical cumulants of the currents and their responses at arbitrary orders in the deviations from equilibrium. Remarkably, such relations have been recently analyzed by means of Euler's polynomials. Here we show that fluctuation relations can actually be explicitly written in terms of the constant terms of these particular polynomials. We hence demonstrate that Euler's polynomials are indeed fundamentally rooted in fluctuation relations, both in the absence and the presence of an external magnetic field.

show abstract

“…Therefore, we first treat in subsection 5.1 the non-trivial case of the antisymmetric relations (48). We then apply in subsection 5.2 the known results of [8,33] to the symmetric relations (47).…”

Section: Independent Quantitiesmentioning

confidence: 99%

“…In addition, we explicitly write the remaining dependent quantities as linear combinations of the independent ones, the coefficients of which being related to Euler polynomials. The main outcome of our work is thus to generalize the findings of [8,33], where no magnetic field is considered, to the case of a nonzero magnetic field. This paper begins with a concise discussion of FR in section 2, before we introduce the statistical cumulants and their responses to the nonequilibrium constraints in section 3.…”

Section: Introductionmentioning

confidence: 98%

See 1 more Smart Citation

Microreversibility and nonequilibrium response theory in magnetic fields

Barbier¹,

Gaspard²

2018

J. Phys. A: Math. Theor.

Self Cite

View full text Add to dashboard Cite

For open systems subjected to external magnetic fields, relations between the statistical cumulants of their fluctuating currents and their response coefficients are established at arbitrary orders in the deviations from equilibrium, as a consequence of microreversibility. These relations are systematically deduced from the extension of the fluctuation relation for this class of systems, and analyzed by using methods developed in [M. Barbier and P. Gaspard, J. Phys. A: Math. Theor. 51 (2018) 355001]. We unambiguously identify, among the statistical cumulants and their nonequilibrium responses, which of these quantities are independent and thus left unspecified by the fluctuation relation, i.e. by microreversibility. We also find the explicit expression of the dependent quantities in terms of the independent ones by means of coefficients of Euler polynomials.

show abstract

Microreversibility, nonequilibrium current fluctuations, and response theory

Cited by 22 publications

References 52 publications

Microreversibility, fluctuations, and nonlinear transport in transistors

Microreversibility, fluctuations, and nonlinear transport in transistors

Microreversibility, nonequilibrium response, and Euler’s polynomials

Microreversibility and nonequilibrium response theory in magnetic fields

Contact Info

Product

Resources

About