NEQ system

4. Heat dissipation = entropy production Surrounding environment NEQ system

5. We study two paradigmatic models for driven systems sketched in figure 1 Asymmetric Random Walk Brownian motion in periodic potential

6. Two main approaches are discussed in the literature Donsker-Varadhan theory Freidlin-Wentzell theory For

7. The purpose of this work is twofold The first Freidlin-Wentzell theory Donsker-Varadhan theory The second

8. Two theoretical explanations for the physical origin of the kink) 1. Pleimling and co-workers (Ref. 22, 23)

9. Two theoretical explanations for the physical origin of the kink) 1. Pleimling and co-workers (Ref. 22, 23)

10. Two theoretical explanations for the physical origin of the kink) 1. Pleimling and co-workers (Ref. 22, 23)

11. Two theoretical explanations for the physical origin of the kink) 2. Budini(Ref. 24)

12. : The numbers of hops to the +(-) direction : The distance

14. for for

15. for 1/z -1/z

16. for 1/z -1/z

18. Path probability with n nN n0 n1 n2 t 0 Dt 2Dt NDt ·· ·

19. with with

21. for for

22. for for

24. for

27. Solve 1. Solving eigenvalue problem directly [18] 2. Ritz variational method [30]

28. Path probability Stochastic action with Effective potential

29. Effective potential

30. Find Since For fixed

32. Constant of motion

33. For small Small < a machine precision The calculation breaks down!! For

35. For large For large even for smaller rates

36. For

38. For , LDF agrees with ARW

40. For