Hamiltonian flocks: Time-Reversal Symmetry and its consequences

TL;DR

This paper demonstrates a generalized time-reversal symmetry in Hamiltonian flocks, leading to a modified fluctuation-dissipation theorem and insights into their non-equilibrium behavior.

Contribution

It reveals a new form of time-reversal symmetry in Hamiltonian flocks, resulting in a generalized fluctuation-dissipation theorem and revised Onsager relations.

Findings

The system obeys a generalized fluctuation-dissipation theorem mixing position and polarity.

It exhibits Onsager-Casimir reciprocity instead of standard Onsager relations.

A non-trivial long-time spin diffusion constant is observed.

Abstract

The fluctuation-dissipation theorem is a hallmark of equilibrium system that stem from their time-reversal symmetry. In many non-equilibrium systems, in particular active ones, extensions and explicit violations of this theorem are used to assess their ''distance'' to equilibrium. In Hamiltonian flocks, conservative yet non-Galilean models of polar liquids, previous work reported collective motion without the activity that usually underlies it. In this paper, we show that this model obeys a generalized time-reversal symmetry that yields a fluctuation-dissipation theorem that mixes position and polarity degrees of freedom. Due to the oddness of spin under time reversal, the system also obeys Onsager-Casimir reciprocity rather than standard Onsager relations. The coupling also induces rich spin orientation dynamics, including a non-trivial diffusion constant at long times. Finally, we show that considering the na\"ive time-reversal operation rather than the generalized one that leaves the system invariant leads to a spurious entropy production rate, that could be wrongly interpreted as a distance to equilibrium. Our findings suggest looking for possible extensions of time-reversal symmetry in active-looking systems, which may lead to yet unknown generalizations of the fluctuation-dissipation theorem.