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Force-free kinetic inference of entropy production

Estimating entropy production, which quantifies irreversibility and energy dissipation, remains a significant challenge despite its central role in nonequilibrium physics. We propose a novel method for estimating the mean entropy production rate $σ$ that relies solely on position traces, bypassing the need for flux or microscopic force measurements. Starting from a recently introduced variance sum rule, we express $σ$ in terms of measurable steady-state correlation functions which we link to previously studied kinetic quantities, known as traffic and inflow rate. Under realistic constraints of limited access to dynamical degrees of freedom, we derive efficient bounds on $σ$ by leveraging the information contained in the system's traffic, enabling partial but meaningful estimates of $σ$. We benchmark our results across several orders of magnitude in $σ$ using two models: a linear stochastic system and a nonlinear model for spontaneous hair-bundle oscillations. Our approach offers a practical and versatile framework for investigating entropy production in nonequilibrium systems.