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Current with "wrong" sign and phase transitions. (arXiv:1810.04639v1 [math-ph])
来源于:arXiv
We prove that under certain conditions, phase separation is enough to sustain
a regime in which current flows along the concentration gradient, a phenomenon
which is known in the literature as \textit{uphill diffusion}. The model we
consider here is a version of that proposed in [G. B. Giacomin, J. L. Lebowitz,
Phase segregation dynamics in particle system with long range interactions,
Journal of Statistical Physics 87(1) (1997): 37-61], which is the continuous
mesoscopic limit of a $1d$ discrete Ising chain with a Kac potential. The
magnetization profile lies in the interval
$\left[-\varepsilon^{-1},\varepsilon^{-1}\right]$, $\varepsilon>0$, staying in
contact at the boundaries with infinite reservoirs of fixed magnetization
$\pm\mu$, $\mu\in(m^*\left(\beta\right),1)$, where
$m^*\left(\beta\right)=\sqrt{1-1/\beta}$, $\beta>1$ representing the inverse
temperature. At last, an external field of Heaviside-type of intensity
$\kappa>0$ is introduced. According to the axiomatic non 查看全文>>