The validity of the fluctuation relations (FRs) for systems in a constant magnetic field is investigated. Recently introduced time-reversal symmetries that hold in the presence of static electric and magnetic fields and of deterministic thermostats are used to prove the transient FRs without invoking, as commonly done, inversion of the magnetic field. Steady-state FRs are also derived, under the $t$-mixing condition. These results extend the predictive power of important statistical mechanics relations. We illustrate this via the nonlinear response for the cumulants of the dissipation, showing how the alternative FRs enable one to determine analytically null cumulants also for systems in a single magnetic field.

中文翻译：

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恒定磁场下系统的涨落关系

研究了恒定磁场下系统波动关系（FRs）的有效性。最近引入的在静电场和磁场以及确定性恒温器存在下保持的时间反转对称性可用于证明瞬态FR，而无需像通常那样进行磁场反转。稳态FR也可以根据$Ť$-混合条件。这些结果扩展了重要统计力学关系的预测能力。我们通过对耗散累积量的非线性响应进行了说明，显示了替代FR如何使一个磁场也能够确定分析上无效的累积量。