Tham khảo tài liệu 'thermodynamics kinetics of dynamic systems part 11', kỹ thuật - công nghệ, cơ khí - chế tạo máy phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | Time Evolution of a Modified Feynman Ratchet with Velocity-Dependent Fluctuations and the Second Law of Thermodynamics 289 to the Zhang 1 formulation of the second law is a challenge to all formulations 6s-6ff thereof and hence a challenge to the second law 6dd . By contrast particularly in the quantum regime 6s-6ff a challenge to any other formulation s 6s-6ff of the second law i may or ii may not be a challenge to the Zhang 1 formulation thereof and hence to all formulations thereof and hence may be a challenge respectively i to the second law 6dd or ii merely to a second law 6dd . And a true challenge must be to the not merely to a second law. There has recently been discovered a classical situation 6gg wherein the minimal-work-principle formulation of the second law can be invalid. The minimal-work-principle formulation of the second law has previously been investigated in the quantum regime where it also can be invalid 6v 6w . But this is not applicable insofar as this present chapter is concerned and in any case does not alter the maximally strong status of the Zhang 1 formulation of the second law. 4. Details of Markovian time evolution and maximization of challenges to the second law Time evolution is complete at N 1 if F R 1 0 A ln2. This corresponds to an overall probability considering both Forward and Reverse DP Brownian motion of 2 correct to first order in V c for all N 1 and exact at N 0 that any given pawl-peg interaction is either a jump or a bounce . to P F R 1 0 A ln2 N P F R 1 0 A ln2 N 2 correct to first order in V c for all N 1 and exact at N 0 . As F R 1 H 1 A H 0 pawl-peg bounces become ever rarer and hence time evolution becomes ever slower. As F R 1 H 1 A H TO pawl-over-peg jumps become ever rarer and hence time evolution becomes ever slower. Time evolution of V N and P V n 2 and likewise of V n and P V n P V mw towards final steady-state values as N H TO is monotonic and asymptotic if 0 F R 1 1 ln2 A 0 diminishing-oscillatory if 1 F R
