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Fluctuation-Dissipation Relations in the absence of Detailed Balance: formalism and applications to Active Matter

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We present a comprehensive study about the relationship between the way Detailed Balance is broken in non-equilibrium systems and the resulting violations of the Fluctuation-Dissipation Theorem. Starting from stochastic dynamics with both odd and even variables under Time-Reversal, we exploit the relation between entropy production and the breakdown of Detailed Balance to establish general constraints on the non-equilibrium steady-states (NESS), which relate the non-equilibrium character of the dynamics with symmetry properties of the NESS distribution. This provides a direct route to derive extended Fluctuation-Dissipation Relations, expressing the linear response function in terms of NESS correlations. Such framework provides a unified way to understand the departure from equilibrium of active systems and its linear response. We then consider two paradigmatic models of interacting self-propelled particles, namely Active Brownian Particles (ABP) and Active Ornstein-Uhlenbeck Particles (AOUP). We analyze the non-equilibrium character of these systems (also within a Markov and a Chapman-Enskog approximation) and derive extended Fluctuation-Dissipation Relations for them, clarifying which features of these active model systems are genuinely non-equilibrium.

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DAL CENGIO, Sara, LEVIS, Demian and PAGONABARRAGA MORA, Ignacio. Fluctuation-Dissipation Relations in the absence of Detailed Balance: formalism and applications to Active Matter. Journal of Statistical Mechanics: Theory and Experiment. 2021. Vol. 4, num. 043201. ISSN 1742-5468. [consulted: 16 of August of 2026]. Available at: https://hdl.handle.net/2445/184759

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