# Canonical quantization of classical systems with generalized entropies

Source: [Canonical quantization of classical systems with generalized entropies](<https://www.sota2.com/research/paper/68fa26e12c2a3760193be3c7>)

Collection index: [llms.txt](<https://www.sota2.com/research/llms.txt>)

Data updated: 2025-10-24T11:40:29.716Z

Authors: A.M. Scarfone

Published: 2005-03-29T17:45:41.000Z

## Abstract

We present, in the framework of the canonical quantization, a class of nonlinear Schroedinger equations with a complex nonlinearity describing, in the mean field approximation, systems of collectively interacting particles. The quantum evolution equation is obtained starting from the study of a N-body classical system where the underlined nonlinear kinetics is governed by a kinetic interaction principle (KIP) recently proposed \[G. Kaniadakis: Physica A 296 (2001), 405--425\]. The KIP, both imposes the form of the generalized entropy associated to the classical system, and determines the Fokker-Planck equation describing the kinetic evolution of the system towards equilibrium.   Keywords: Nonlinear Schroedinger equation, Nonlinear kinetics, Generalized entropy.

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## Original sources and implementation

[Original paper](<https://arxiv.org/abs/cond-mat/0503684>)

[PDF](<https://arxiv.org/pdf/cond-mat/0503684.pdf>)