A geometric description of some thermodynamical systems

Summary

The paper introduces a geometric description of thermodynamical systems using almost cosymplectic structures, which are a natural framework to study these systems. The authors obtain the same evolution equations as those obtained by Gay-Balmaz and Yoshimura using variational arguments.

Highlights

• Almost cosymplectic structures are used to describe thermodynamical systems.
• The authors obtain the same evolution equations as Gay-Balmaz and Yoshimura.
• The geometric description allows for the application of geometric tools.
• The paper considers adiabatically closed simple systems, systems with internal mass transfer, and open simple thermodynamic systems.
• The Legendre transformation is used to relate the Lagrangian and Hamiltonian descriptions.
• The paper introduces a generalization of almost cosymplectic structures of higher order.
• The authors discuss the potential for further research, including the study of submanifolds and the identification of almost Poisson brackets.

Key Insights

• The use of almost cosymplectic structures provides a new mathematical description of thermodynamical systems, which can be used to study the dynamics of these systems.
• The paper shows that the evolution equations obtained using this geometric description are equivalent to those obtained by Gay-Balmaz and Yoshimura using variational arguments.
• The geometric description allows for the application of geometric tools, such as the Legendre transformation, to study the dynamics of thermodynamical systems.
• The paper introduces a generalization of almost cosymplectic structures of higher order, which can be used to describe more complex thermodynamical systems.
• The authors discuss the potential for further research, including the study of submanifolds and the identification of almost Poisson brackets, which can provide new insights into the dynamics of thermodynamical systems.
• The paper highlights the importance of considering the geometric structure of thermodynamical systems, which can provide a deeper understanding of the dynamics of these systems.
• The use of almost cosymplectic structures can provide a new perspective on the study of thermodynamical systems, which can lead to new insights and results.

Mindmap

Citation

de León, M., & Bajo, J. (2024). A geometric description of some thermodynamical systems (Version 1). arXiv. https://doi.org/10.48550/ARXIV.2412.18478