Dresden 2026 – scientific programme
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BP: Fachverband Biologische Physik
BP 32: Statistical Physics of Biological Systems III (joint session BP/DY)
BP 32.9: Talk
Thursday, March 12, 2026, 17:15–17:30, BAR/SCHÖ
Ergodicity shapes inference in biological reactions driven by a latent trajectory — •Ricardo Martinez-Garcia1, Benjamin Garcia de Figueiredo2, Justin Calabrese1, and William Fagan3 — 1CASUS-HZDR, Görlitz, Germany. — 2Princeton University, Princeton NJ, USA. — 3University of Maryland, College Park MD, USA.
Many natural phenomena, from intracellular reactions to predator-prey encounters, can be described as counts of events triggered at random intervals when an underlying dynamical system enters reactive regions of its phase space. These reactions control biological functions across scales, from cellular processes to ecosystem services and stability. We compute the exact distribution of inter-count times under the only assumption that the latent dynamical system is Markovian and ergodic, recovering widely used Poisson statistics as a limiting case. These results limit what information about the latent process can be inferred from a local detector, which we explore in two biophysical scenarios. First, in estimating an animal's activity from detector crossings, we show that mean counts may fail to capture movement parameters, encoded in higher-order moments. Second, we show that the variance of inter-reaction times imposes a fundamental limit on how precisely detector measurements can infer the size of an ensemble of trajectories, generalizing the Berg-Purcell limit for chemosensation. Overall, we develop a flexible framework for quantifying inter-event time distributions in reaction-diffusion systems that shows which properties of latent processes are inferable from observed reactions.
Keywords: Renewal processes; First passage statistics; Biological reactions; Cell sensing; Reaction-diffusion processes