这是一份 Imperial帝国理工大学 PHYS96008作业代写的成功案例
Additionally all path-specific departure rates are non-negative so we write
$$
h=\left(h_{\mathrm{p}}: p \in P\right) \geq 0
$$
where $P$ is the set of all network paths. As a consequence
$$
\Psi_{n}\left(t, h^{}\right)>v_{i i} p \in P_{i i} \Rightarrow h_{n}^{}=0 .
$$
as can easily be proven from by contradiction. We next comment that the relevant notion of flow conservation is
$$
\sum_{p \in P_{j}} \int_{0}^{T} h_{\mathrm{p}}(t) \mathrm{d} t=Q_{i j} \quad \forall(i, j) \in W
$$
where $Q_{i j}$ is the fixed travel demand (expressed as a traffic volume) for $(i, j) \in W$. Thus, the set of feasible solutions is
PHYS96008 COURSE NOTES ：
We can then seek to work with the free energy and the model Then:
$$
F=-[N / \beta] \log Z
$$
We can also explore the standard method of calculating state functions from the free energy: ${ }^{9}$
$$
\begin{aligned}
&P=-(\partial F / \partial A){T} \ &S=-(\partial F / \partial T){A}
\end{aligned}
$$
or, using:
$$
S=-k \beta^{2}(\partial F / \partial \beta)_{A}
$$