The statistical foundation of entropy in extended irreversible thermodynamics

摘要: In the theory of extended irreversible thermodynamics (EIT), flux-dependent entropy function plays a key role and has fundamental distinction from usual flux-independent adopted by classical (CIT). However, its existence, as prerequisite for EIT, statistical origin have never been justified. this work, studying macroscopic limit an \epsilon-dependent Langevin dynamics, which admits large deviations (LD) principle, we show that stationary LD rate functions probability density p_{\epsilon}(x; t) joint \dot{x}; actually turn out to be desired fluxindependent in CIT EIT respectively. The difference two is determined time resolution Brownian motions times Lagrangian, latter arises Hamilton-Jacobi equation can used constructing conserved Lagrangian/Hamiltonian dynamics.