Microreversibility and nonequilibrium response theory in magnetic fields

TL;DR

This paper derives relations between cumulants and response coefficients for open systems in magnetic fields, extending fluctuation relations to all orders and clarifying dependencies among statistical quantities.

Contribution

It systematically extends fluctuation relations to nonequilibrium systems with magnetic fields and identifies independent versus dependent cumulants and responses.

Findings

Relations between cumulants and responses are established at all orders.

Explicit expressions for dependent quantities are derived using Euler polynomial coefficients.

The analysis clarifies which statistical quantities are constrained by microreversibility.

Abstract

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.