# Thermodynamic Behavior of Statistical Event Counting in Time: Independent and Correlated Measurements

@inproceedings{Qian2021ThermodynamicBO, title={Thermodynamic Behavior of Statistical Event Counting in Time: Independent and Correlated Measurements}, author={Hong Qian}, year={2021} }

We introduce an entropy analysis of time series, repeated measurements of statistical observables, based on an Eulerian homogeneous degree-one entropy function Φ(t, n) of time t and number of events n. The duality of Φ, in terms of conjugate variables η = −Φt and μ = Φn, yields an “equation of state” (EoS) in differential form that resembles the Gibbs-Duhem relation in classical thermodynamics: tdη − ndμ = 0. For simple Poisson counting with rate r, η = r(e−1). The conjugate variable η is then… Expand

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