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Updated: Jan 10, 2026

Cross-Modal Multivariate Pattern Analysis
Published on: November 9, 2011
Revising the theory of cross phenomena
1Department of Materials Science and Engineering, The Pennsylvania State University, University Park, PA 16802, United States of America.
The revised theory of cross phenomena (TCP) uses the first law of thermodynamics to derive independent flux equations. This thermodynamic approach corrects flaws in previous phenomenological models.
Area of Science:
- Thermodynamics
- Physical Chemistry
- Non-equilibrium Systems
Background:
- Previous work utilized a combined law of thermodynamics.
- Potentials in the combined law were not independent.
- Phenomenological Onsager flux equations have known flaws.
Purpose of the Study:
- To revise the theory of cross phenomena (TCP).
- To derive flux equations from fundamental thermodynamic laws.
- To establish flux equations based on independent driving forces.
Main Methods:
- Revision of the theory of cross phenomena (TCP).
- Application of the first law of thermodynamics.
- Derivation of flux equations from fundamental principles.
Main Results:
- The revised TCP starts from the first law of thermodynamics.
- Flux equations are derived with respect to independent driving forces.
- The revised TCP demonstrates flaws in phenomenological Onsager flux equations.
Conclusions:
- The revised TCP provides a more rigorous foundation for flux equations.
- Fundamental thermodynamic laws are preferable to phenomenological approaches.
- The revised theory offers a corrected framework for cross-phenomena analysis.
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