258 I will consider the problem of minimized (expected) dissipated work or released heat in systems described by over-damped Langevin equation. The problem can be mathematically stated as a standard stochastic optimization problem, but turns out to have a suprisingly simple solution in turns of Burgers equation (or nonlinear diffusion equation) for an auxiliary field, and mass transport by the corresponding velocity field [1]. One application of these results is an improvement of Landauer's bound on the heat released when setting one bit, if it has to be done in a finite time [2]. The refined bound has the form of T log2 + K/t, where T log 2 is the Landauer bound, t is the time of the process and K can be computed from the initial and final states and an appropriate solution of Burgers equation. If temperature and/or the friction coefficient are not constant in time and/or space a similar almost closed formula can be derived, not from the released heat but for the entropy production in the environment [3]. I will discuss the conceptual issues we have encountered in this direction. [1] Erik Aurell, Carlos Mejia-Monasterio, Paolo Muratore-Ginanneschi, Phys. Rev. Lett. 106, 250601 (2011) [2] Erik Aurell, Krzysztof Gawȩdzki, Carlos Mejía-Monasterio, Roya Mohayaee, Paolo Muratore-Ginanneschi [arXiv:1201.3207] [3] Stefano Bo, Erik Aurell, Antonio Celani and Ralf Eichhorn (2012, in preparation). The 3rd Nordic Workshop on Statistical Physics: Biological, Complex and Non-Equilibrium Systems Erik Aurell eaurell@kth.se None