Low-dissipation engines: Microscopic construction via shortcuts to adiabaticity and isothermality, the optimal relation between power and efficiency.

We construct a microscopic model of low-dissipation engines by driving a Brownian particle in a time-dependent harmonic potential. Shortcuts to adiabaticity and shortcuts to isothermality are introduced to realize the adiabatic and isothermal branches in a thermodynamic cycle, respectively. We derive an analytical formula of the efficiency at maximum power with explicit expressions of dissipation coefficients under the optimized protocols. When the relative temperature difference between the two baths in the cycle is insignificant, this expression satisfies the universal law of efficiency at maximum power up to the quadratic term of the Carnot efficiency. For large relative temperature differences, the efficiency at maximum power tends to be 1/2. Furthermore, we analyze the issue of power at any given efficiency for general low-dissipation engines and then obtain the supremum of the power in three limiting cases, respectively. These expressions of maximum power at given efficiency provide the optimal relations between power and efficiency which are tighter than the results in previous references.