Living and non-living active matter consumes energy at the microscopic scale to drive emergent, macroscopic behavior including traveling waves and coherent oscillations. Recent work has characterized non-equilibrium systems by their total energy dissipation, but little has been said about how dissipation manifests in distinct spatiotemporal patterns. We introduce a measure of irreversibility we term the entropy production factor to quantify how time reversal symmetry is broken in field theories across scales. We use this scalar, dimensionless function to characterize a dynamical phase transition in simulations of the Brusselator, a prototypical biochemically motivated non-linear oscillator. We measure the total energetic cost of establishing synchronized biochemical oscillations while simultaneously quantifying the distribution of irreversibility across spatiotemporal frequencies.

生命和非生命活性物质在微观尺度上消耗能量，以驱动出现的宏观行为，包括行波和相干振荡。最近的工作以总能量耗散为非平衡系统的特征，但是关于耗散如何以不同的时空模式表现出来却鲜有报道。我们引入了不可逆性的度量，我们称其为熵产生因子，以量化跨规模的场论如何打破时间逆向对称性。我们使用这种无量纲的无量纲函数来表征Brusselator（一种典型的生化动力非线性振荡器）的仿真中的动态相变。