Certain physical systems require Lagrangians not of the standard kinetic minus potential form
Certain physical systems, such as dissipative, non-conservative, or heavily damped mechanical and thermodynamic systems, require non-standard Lagrangians that do not take the traditional kinetic minus potential form.
The claim proposes that certain physical systems require non-standard Lagrangians rather than the conventional kinetic minus potential form. Multiple retrieved papers explicitly discuss non-standard Lagrangians, contact Lagrangians, and generalized variational principles designed specifically to handle dissipative, non-conservative, and complex multi-energy systems where standard Lagrangians are insufficient. Thus, the evidence strongly supports the claim.
Jordi Gaset Rifà, M. Lainz, Arnau Mas, Xavier Rivas. The Herglotz variational principle for dissipative field theories. 2022. https://doi.org/10.1142/S2972458924500060
The Herglotz variational principle generalizes contact Lagrangians for dissipative field theories beyond the standard kinetic minus potential form.
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Diana T. Pham, Zdzislaw E. Musielak. Non-Standard and Null Lagrangians for Nonlinear Dynamical Systems and Their Role in Population Dynamics. 2023. https://doi.org/10.3390/math11122671
Non-standard Lagrangians for damped nonlinear systems do not display standard energy-like terms while reproducing correct equations of motion.
Xu K, Qi Y, Sun C, Ai D, Wang J, He W, Yang F, Ren H. Exergy Flow as a Unifying Physical Quantity in Applying Dissipative Lagrangian Fluid Mechanics to Integrated Energy Systems.. 2024. https://doi.org/10.3390/e26090791
Modified Lagrangian mechanics uses exergy flow as a unifying Lagrangian to capture multi-energy systems with mechanical and thermal dissipations.
R. El-Nabulsi, W. Anukool. Helmholtz and Liénard-type oscillators from non-standard Lagrangians. 2026. https://doi.org/10.15625/0866-7136/22664
Non-standard Lagrangians provide a variational framework for systems with velocity-dependent nonlinearities and dissipation that traditional formulations miss.
Ren H. A Variational Formulation for Irreversible Thermodynamics with Path Dependence.. 2026. https://doi.org/10.3390/e28010094
Path-dependent energy Lagrangians for irreversible thermomechanics incorporate heat, entropy, and dissipation directly into the action without standard Rayleigh potentials.
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