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In this paper, the first insights into a variational formulation of stochastic thermodynamics are presented for finite-dimensional Langevin systems. Following the variational approach in [4], the fundamental variational principle of classical mechanics is systematically extended to include irreversible and stochastic forces. By including thermodynamic entropy as an independent state variable in phase space, the conditions for thermodynamic consistency are derived extending the tools of stochastic thermodynamics, providing a new fluctuation-dissipation relation. The method is illustrated through a thermomechanical system.

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Variational Approach to the Stochastic Thermodynamics of Langevin Systems

  • 会议论文

  • 发表日期：

    2026年

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  • Héctor Vaquero del Pino,
  • François Gay-Balmaz,
  • Hiroaki Yoshimura,
  • Lock Yue Chew

摘要

In this paper, the first insights into a variational formulation of stochastic thermodynamics are presented for finite-dimensional Langevin systems. Following the variational approach in [4], the fundamental variational principle of classical mechanics is systematically extended to include irreversible and stochastic forces. By including thermodynamic entropy as an independent state variable in phase space, the conditions for thermodynamic consistency are derived extending the tools of stochastic thermodynamics, providing a new fluctuation-dissipation relation. The method is illustrated through a thermomechanical system.