Nambu Nonequilibrium Thermodynamics and the Lyapunov Structure of Open Systems

@misc{katagiri2026nambu,
  title = {{Nambu Nonequilibrium Thermodynamics and the Lyapunov Structure of Open Systems}},
  author = {So Katagiri},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2606.05231},
  eprint = {2606.05231},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2606.05231},
}

TY  - UNPB
TI  - Nambu Nonequilibrium Thermodynamics and the Lyapunov Structure of Open Systems
AU  - So Katagiri
PY  - 2026
DA  - 2026/10/12
PB  - arXiv
DO  - 10.48550/arxiv.2606.05231
UR  - https://arxiv.org/abs/2606.05231
AB  - We investigate the thermodynamic meaning of the dissipation potential in Nambu nonequilibrium thermodynamics (NNET) using a simple open-piston model. The system is described by three variables: the gas volume, the piston momentum, and the thermodynamic entropy of the gas. The reversible dynamics is formulated in terms of two Nambu Hamiltonians, the extended energy and the thermodynamic entropy, while the irreversible dynamics is generated by a bath-relative Massieu-type dissipation potential through a positive-semidefinite gradient flow. This construction reproduces the physical processes of frictional heating and heat exchange with the reservoir while preserving their thermodynamic interpretation. We show that the time derivative of the dissipation potential coincides with the total entropy production rate of the system and the heat bath. Although the subsystem entropy may evolve nonmonotonically, the dissipation potential is a Lyapunov function under the conditions realized in this model. These results provide an explicit thermodynamic interpretation of the dissipation potential and its associated Lyapunov structure within NNET.
ER  -