Microcanonical Ensemble and Algebra of Conserved Generators for Generalized Quantum Dynamics

TL;DR

This paper develops a microcanonical ensemble framework for generalized quantum dynamics, linking conserved generators to the algebraic structure and stability of quantum field configurations in statistical mechanics.

Contribution

It introduces a microcanonical ensemble approach for generalized quantum dynamics, enabling analysis of entropy, free energy, and algebraic structures of conserved generators.

Findings

Constructed a microcanonical ensemble for generalized quantum dynamics.

Defined microcanonical entropy and free energy for quantum fields.

Analyzed the algebra of conserved generators and phase space flows.

Abstract

It has recently been shown, by application of statistical mechanical methods to determine the canonical ensemble governing the equilibrium distribution of operator initial values, that complex quantum field theory can emerge as a statistical approximation to an underlying generalized quantum dynamics. This result was obtained by an argument based on a Ward identity analogous to the equipartition theorem of classical statistical mechanics. We construct here a microcanonical ensemble which forms the basis of this canonical ensemble. This construction enables us to define the microcanonical entropy and free energy of the field configuration of the equilibrium distribution and to study the stability of the canonical ensemble. We also study the algebraic structure of the conserved generators from which the microcanonical and canonical ensembles are constructed, and the flows they induce on the phase space.