  We discuss the Monge problem of mass transportation in the framework of
stochastic thermodynamics and revisit the problem of the Landauer limit for
finite-time thermodynamics, a problem that got the interest of Krzysztof
Gawedzki in the last years. We show that restricted to one dimension, optimal
transportation is efficiently solved numerically by well known methods from
differential equations. We add a brief discussion about the relevance this has
on optimising the processing in modern computers.
