Thermodynamic Tree: The Space of Admissible Paths

Details Thermodynamic Tree: The Space of Admissible Paths Thermodynamic Tree: The Space of Admissible Paths

2012-01-30

arxiv.org/abs/1201.6315v2

Physics

Condensed Matter

Statistical Mechanics

Extended version, 29 pages,8 figures, 67 cited references

Scientific paper

Is a spontaneous transition from a state x to a state y allowed by thermodynamics? Such a question arises often in chemical thermodynamics and kinetics. We ask the more formal question: is there a continuous path between these states, along which the conservation laws hold, the concentrations remain non-negative and the relevant thermodynamic potential G (Gibbs energy, for example) monotonically decreases? The obvious necessary condition, G(x)\geq G(y), is not sufficient, and we construct the necessary and sufficient conditions. For example, it is impossible to overstep the equilibrium in 1-dimensional (1D) systems (with n components and n-1 conservation laws). The system cannot come from a state x to a state y if they are on the opposite sides of the equilibrium even if G(x) > G(y). We find the general multidimensional analogue of this 1D rule and constructively solve the problem of the thermodynamically admissible transitions. We study dynamical systems, which are given in a positively invariant convex polyhedron and have a convex Lyapunov function G. An admissible path is a continuous curve along which $G$ does not increase. For x,y from D, x>y (x precedes y) if there exists an admissible path from x to y and x \sim y if x>y and y>x. The tree of G in D is a quotient space D/~. We provide an algorithm for the construction of this tree. In this algorithm, the restriction of $G$ onto the 1-skeleton of $D$ (the union of edges) is used. The problem of existence of admissible paths between states is solved constructively. The regions attainable by the admissible paths are described.

Affiliated with

Also associated with

No associations

Rating

Thermodynamic Tree: The Space of Admissible Paths does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Thermodynamic Tree: The Space of Admissible Paths, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Thermodynamic Tree: The Space of Admissible Paths will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-360413