  One of the main objectives of science is the recognition of a general pattern
in a particular phenomenon in some particular regime. In this work, this is
achieved with the analytical expression for the optimal protocol that minimizes
the thermodynamic work and its variance for finite-time, isothermal, and weak
processes. The method that solves the Euler-Lagrange integral equation is quite
general and depends only on the time-reversal symmetry of the optimal protocol,
which is proven generically for the regime considered. The solution is composed
of a straight line with jumps at the boundaries and impulse-like terms. Already
known results are deduced, and many new examples are solved corroborating this
pattern. Slowly-varying and sudden cases are deduced in their appropriate
asymptotic limits. Comparison with numerical procedures is limited by the
nonavailability of the present methods of the literature to produce solutions
in the space of distributions.
