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  • 1State Key Laboratory of Disaster Reduction in Civil Engineering, College of Civil Engineering, Tongji University, Shanghai 200092, China.

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Summary
This summary is machine-generated.

This study presents a new energy Lagrangian for irreversible thermomechanics, unifying heat and entropy accounting within a single action. This framework ensures consistent, positive entropy production across coupled dissipative processes.

Keywords:
continuum thermodynamicsentropy productionirreversible processespath-dependent actionvariational thermodynamics

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Area of Science:

  • Thermodynamics
  • Continuum Mechanics
  • Mathematical Physics

Background:

  • Irreversible processes in thermomechanics lack a unified variational framework.
  • Existing models often require complex additions like Lagrange multipliers or Rayleigh potentials.
  • Accurate accounting of heat and entropy is crucial for understanding dissipative systems.

Purpose of the Study:

  • To introduce a novel path-dependent energy Lagrangian for irreversible thermomechanics.
  • To embed heat and entropy accounting directly into the action integral.
  • To provide a unified variational framework for coupled dissipative phenomena.

Main Methods:

  • Developed a path-dependent energy Lagrangian incorporating heat and entropy.
  • Utilized an explicit θs term for Helmholtz conjugacy and positive heat capacity.
  • Formulated heat as a divergence to yield natural flux.
  • Introduced a history integral for upper-limit variation and entropy production.
  • Applied stationarity to derive field equations and balance laws.

Main Results:

  • The formulation naturally incorporates Helmholtz conjugacy and positive heat capacity.
  • Nonnegative dissipative productions are modularized into a single term.
  • Stationarity yields standard field equations, global entropy balance, and channel-wise power identity.
  • Classical closures for heat conduction, diffusion, and viscous mechanics emerge as special cases.
  • The framework demonstrates unified action, entropy audit, and consistent positive production.

Conclusions:

  • The proposed Lagrangian offers a unified variational approach to irreversible thermomechanics.
  • It simplifies the formulation by eliminating the need for Lagrange multipliers or Rayleigh potentials.
  • The framework consistently handles coupled dissipative mechanisms, ensuring positive entropy production.