Microreversibility, nonequilibrium response, and Euler's polynomials

TL;DR

This paper reveals that Euler's polynomials are fundamentally connected to fluctuation relations in nonequilibrium systems constrained by microreversibility, applicable even with external magnetic fields.

Contribution

It explicitly links fluctuation relations to the constant terms of Euler's polynomials, deepening understanding of microreversibility in nonequilibrium physics.

Findings

Fluctuation relations can be expressed via Euler's polynomials.

Euler's polynomials underpin fluctuation relations with magnetic fields.

Constant terms of Euler's polynomials relate to fluctuation symmetries.

Abstract

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.