Aurell Erik, Mejía-Monasterio Carlos, Muratore-Ginanneschi Paolo
ACCESS Linnaeus Centre, KTH, Stockholm, Sweden and Department of Computational Biology, AlbaNova University Centre, S-106 91 Stockholm, Sweden.
Phys Rev E Stat Nonlin Soft Matter Phys. 2012 Feb;85(2 Pt 1):020103. doi: 10.1103/PhysRevE.85.020103. Epub 2012 Feb 6.
We study the problem of optimizing released heat or dissipated work in stochastic thermodynamics. In the overdamped limit these functionals have singular solutions, previously interpreted as protocol jumps. We show that a regularization, penalizing a properly defined acceleration, changes the jumps into boundary layers of finite width. We show that in the limit of vanishing boundary layer width no heat is dissipated in the boundary layer, while work can be done. We further give an alternative interpretation of the fact that the optimal protocols in the overdamped limit are given by optimal deterministic transport (Burgers equation).
我们研究了随机热力学中释放热量或耗散功的优化问题。在过阻尼极限下，这些泛函具有奇异解，此前被解释为协议跳跃。我们表明，通过对适当定义的加速度进行惩罚的正则化，可将跳跃转变为有限宽度的边界层。我们证明，在边界层宽度趋于零的极限情况下，边界层中不会耗散热量，但可以做功。我们还对过阻尼极限下的最优协议由最优确定性输运（伯格斯方程）给出这一事实给出了另一种解释。
