Recent content by xibeisiber

Nobody?:L:L Google book of Stochastic Energetics: link Is there any problem in the formula A.75(p310) and the first formula in p311?

what's the relation of the grand potential J=F-\mu N and total Helmholtz free energy of "system and particle environment" F^{tot}? In K. Sekimoto's book "Stochastic Energetics" P182, P310 and P311 (see screenshots in the link): Does it mean the followings:J=lim[F_{tot}-\mu N_{tot}]...

the inner product of two vector quantity is certainly a scalar quantity.. $\vec{v}\cdot\vec{v}$

em,I feel like I understand that "on the line" means one dimension. I wasted too much time on such a simple question!:cry:

But the system I consider is 2D,the V(x,y) is not always there for all f(x,y) and g(x,y).So there must be anything else I haven't realized.

Thank you for your reply! I tried to prove that ∂f/∂y=∂g/∂x,as shown in the attachment,but failed...

Show that all vector fields on the line are gradient systems. This is exercise 7.2.4 in the book "Nonlinear Dynamics and Chaos" by Steven H.Strogatz Thanks very much!