Stochastic Thermodynamics: Dissipativity, Losslessness, Accumulativity, Energy Storage, and Entropy Production

Authors

Manuel Lanchares, Wassim M. Haddad

Abstract

In this paper, we develop an energy-based dynamical system model driven by a Markov input process to present a unified framework for stochastic thermo-dynamics predicated on a stochastic dynamical systems formalism. Specifically, using a stochastic dissipativity, losslessness, and accumulativity theory, we develop a nonlinear stochastic port-Hamiltonian system model characterized by energy conservation and entropy nonconservation laws that are consistent with statistical thermodynamic principles. In particular, we show that the difference between the stored system energy and the supplied system energy for our stochastic thermodynamic model is a martingale with respect to the system filtration, whereas the system entropy is a submartingale with respect to the system filtration.

Citation

• Journal: 2023 31st Mediterranean Conference on Control and Automation (MED)
• Year: 2023
• Volume:
• Issue:
• Pages: 61–66
• Publisher: IEEE
• DOI: 10.1109/med59994.2023.10185753

BibTeX

@inproceedings{Lanchares_2023,
  title={{Stochastic Thermodynamics: Dissipativity, Losslessness, Accumulativity, Energy Storage, and Entropy Production}},
  DOI={10.1109/med59994.2023.10185753},
  booktitle={{2023 31st Mediterranean Conference on Control and Automation (MED)}},
  publisher={IEEE},
  author={Lanchares, Manuel and Haddad, Wassim M.},
  year={2023},
  pages={61--66}
}

Download the bib file

References

• Lanchares, M. & Haddad, W. M. Dissipative stochastic dynamical systems. Systems & Control Letters vol. 172 105451 (2023) – 10.1016/j.sysconle.2022.105451
• Sekimoto, K. Kinetic Characterization of Heat Bath and the Energetics of Thermal Ratchet Models. Journal of the Physical Society of Japan vol. 66 1234–1237 (1997) – 10.1143/jpsj.66.1234
• Van Der Schaft, A. J. & Maschke, B. M. On the Hamiltonian formulation of nonholonomic mechanical systems. Reports on Mathematical Physics vol. 34 225–233 (1994) – 10.1016/0034-4877(94)90038-8
• Lanchares, M. & Haddad, W. M. Stochastic Thermodynamics: Dissipativity, Losslessness, Accumulativity, Energy Storage, and Entropy Production. 2023 31st Mediterranean Conference on Control and Automation (MED) 61–66 (2023) doi:10.1109/med59994.2023.10185753 – 10.1109/med59994.2023.10185753
• Haddad, W. M. & Chellaboina, V. Nonlinear Dynamical Systems and Control. (2008) doi:10.1515/9781400841042 – 10.1515/9781400841042
• Willems, J. C. Dissipative dynamical systems part I: General theory. Archive for Rational Mechanics and Analysis vol. 45 321–351 (1972) – 10.1007/bf00276493
• Onsager, L. Reciprocal Relations in Irreversible Processes. II. Physical Review vol. 38 2265–2279 (1931) – 10.1103/physrev.38.2265
• Onsager, L. Reciprocal Relations in Irreversible Processes. I. Physical Review vol. 37 405–426 (1931) – 10.1103/physrev.37.405
• Haddad, W. M., Rajpurohit, T. & Jin, X. Energy-based feedback control for stochastic port-controlled Hamiltonian systems. Automatica vol. 97 134–142 (2018) – 10.1016/j.automatica.2018.07.031
• peliti, Stochastic Thermodynamics: An Introduction. (2021)
• Das Maxwellsche Gesetz der Geschwindigkeitsverteilung in der Relativtheorie. Ann Phys (1911)
• haddad, A Dynamical Systems Theory of Thermodynamics. (2019)
• prigogine, Thermodynamics of Irreversible Processes. (1955)
• de groot, Thermodynamics of Irreversible Processes. (1951)
• Einstein, A. Über die von der molekularkinetischen Theorie der Wärme geforderte Bewegung von in ruhenden Flüssigkeiten suspendierten Teilchen. Annalen der Physik vol. 322 549–560 (1905) – 10.1002/andp.19053220806
• Sekimoto, K. Stochastic Energetics. Lecture Notes in Physics (Springer Berlin Heidelberg, 2010). doi:10.1007/978-3-642-05411-2 – 10.1007/978-3-642-05411-2