What question did this study set out to answer?

To classify the algebraic structure and representations of a three-dimensional commutative nonassociative algebra and construct an integrable quantum toy model exhibiting intrinsic dissipation.

August 16, 2026Open Access

Intrinsic Dissipation in Nonassociative Algebras: Structural Classification of a Three-Dimensional Dissipative Algebra and an Integrable Quantum Toy Model 非结合代数中的内禀耗散:三维耗散代数的结构分类与一个可积量子玩具模型

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ZLZhongqiang Liu

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Overview

Theoretical analysis reveals intrinsic dissipation and qubit dynamics in a nonassociative algebra, demonstrating quantum irreversibility without requiring an external heat bath.

Key Points

To classify the algebraic structure and representations of a three-dimensional commutative nonassociative algebra and construct an integrable quantum toy model exhibiting intrinsic dissipation.
Derived algebraic and representation-theoretic classifications from the axiomatic system e²=1, i²=−1, and ei=0.
Constructed quantum Hamiltonians using left-multiplication operators on a (2+1)-dimensional Minkowski representation space and verified all identities with symbolic computation.
Classified the algebra as simple and power-associative with full matrix algebra M₃(ℝ) multiplication and a unique natural module ℝ³ under a Minkowski metric.
Demonstrated that the Hamiltonian H=Lₑ exactly mirrors standard qubit Rabi oscillations while physical states decouple from ghost directions.
Proved an intrinsic dissipation theorem where an associator operator yields an exact solution with monotonic probability growth P_δ(t)=λ²(cosh t−1)², producing irreversibility without an external reservoir.

Cite This Study

Zhongqiang Liu (2026) studied this question.

synapsesocial.com/papers/6a817a91f2fb91fc834ae7d9 https://doi.org/10.5281/zenodo.21959850

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August 16, 2026Open Access

Intrinsic Dissipation in Nonassociative Algebras: Structural Classification of a Three-Dimensional Dissipative Algebra and an Integrable Quantum Toy Model 非结合代数中的内禀耗散:三维耗散代数的结构分类与一个可积量子玩具模型

View Full Paper

Ask AI

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Authors

ZLZhongqiang Liu

Discussion

Member takes

Overview

Theoretical analysis reveals intrinsic dissipation and qubit dynamics in a nonassociative algebra, demonstrating quantum irreversibility without requiring an external heat bath.

Key Points

To classify the algebraic structure and representations of a three-dimensional commutative nonassociative algebra and construct an integrable quantum toy model exhibiting intrinsic dissipation.
Derived algebraic and representation-theoretic classifications from the axiomatic system e²=1, i²=−1, and ei=0.
Constructed quantum Hamiltonians using left-multiplication operators on a (2+1)-dimensional Minkowski representation space and verified all identities with symbolic computation.
Classified the algebra as simple and power-associative with full matrix algebra M₃(ℝ) multiplication and a unique natural module ℝ³ under a Minkowski metric.
Demonstrated that the Hamiltonian H=Lₑ exactly mirrors standard qubit Rabi oscillations while physical states decouple from ghost directions.
Proved an intrinsic dissipation theorem where an associator operator yields an exact solution with monotonic probability growth P_δ(t)=λ²(cosh t−1)², producing irreversibility without an external reservoir.

Cite This Study

Zhongqiang Liu (2026) studied this question.

synapsesocial.com/papers/6a817a91f2fb91fc834ae7d9 https://doi.org/10.5281/zenodo.21959850

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