Generating functions for irreversible Hamiltonian systems

TL;DR

This paper extends the concept of conservative-irreversible functions to smooth manifolds, exploring their local representations and algebraic structures, with implications for Hamiltonian systems and complex algebras.

Contribution

It introduces an extension of conservative-irreversible functions to smooth manifolds and investigates their local forms and algebraic properties, broadening the theoretical framework.

Findings

Not all conservative-irreversible functions are weighted products of almost Poisson brackets.

Biquadratic functions from these are studied for algebraic structures.

Potential for algebraic frameworks on complex algebras.

Abstract

The definition of conservative-irreversible functions is extended to smooth manifolds. The local representation of these functions is studied and reveals that not each conservative-irreversible function is given by the weighted product of almost Poisson brackets. The biquadratic functions given by conservative-irreversible functions are studied and reveal a possibility for an algebraic framework on arbitrary and in particular complex algebras.