## Abstract

We discuss a mathematical link between the Quantum Statistical Mechanics and the logistic growth and decay processes. It is based on an observation that a certain nonlinear operator evolution equation, which we refer to as the Logistic Operator Equation (LOE), provides an extension of the standard model of noninteracting bosons. We discuss formal solutions (asymptotic formulas) for a special calibration of the LOE, which sets it in the number-theoretic framework. This trick, in the tradition of Julia and Bost-Connes, makes it possible for us to tap into the vast resources of classical mathematics and, in particular, to construct explicit solutions of the LOE via the Dirichlet series. The LOE is applicable to a range of modeling and simulation tasks, from characterization of interacting boson systems to simulation of some complex man-made networks. The theoretical results enable numerical simulations, which, in turn, shed light at the unique complexities of the rich and multifaceted models resulting from the LOE.

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Sowa, A. Interacting Bose gas, the logistic law, and complex networks.
*Russ. J. Math. Phys.* **22**, 98–111 (2015). https://doi.org/10.1134/S1061920815010112

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DOI: https://doi.org/10.1134/S1061920815010112

### Keywords

- Exogenous Variable
- Dirichlet Series
- Prime Decomposition
- Logistic Decay
- Consecutive Word