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DY: Fachverband Dynamik und Statistische Physik

DY 5: Focus Session: Physics of Behavior (joint session SOE/DY)

DY 5.7: Vortrag

Montag, 9. März 2026, 11:30–11:45, GÖR/0226

Emergence of power-laws and the uncertainty principle in human contact duration — •Jun Sun — GESIS - Leibniz Institute for the Social Sciences, Cologne, Germany

Consider the mechanism underlying human contact duration distributions as an aggregate effect of time-homogeneous processes, where the persistent probability of a contact (pairwise or higher-order) is drawn from a distribution but remains constant during its lifetime (Starnini et al., 2013). I propose a thermodynamic interpretation of the model, in which the persistent probability of a contact is mapped to a negative log-energy, identifying time as the inverse temperature, and the duration distribution as the partition function. I prove that under mild conditions, the contact duration distribution exhibits a power-law with potential cutoffs, a phenomenon commonly observed in empirical data. Such distributions are special in the thermodynamic framework as they have constant specific heat capacity, which corresponds to both the power-law exponent and the effective degrees of freedom. When contact agents act independently, the degrees of freedom equal the contact order. Behavioral correlation between agents reduces the effective degrees of freedom (therefore also the power-law exponent). Finally, I establish an uncertainty relation between time and persistent probability, revealing a fundamental limit within which contact durations can be characterized. Unlike the once-controversial notion of temperature fluctuation, the uncertainty of time in contact data is well-defined.

Keywords: contact dynamics; power-law; degrees of freedom; uncertainty principle