The constraint relation for efficiency and power is crucial for the design of optimal heat engines operating within finite time. We find a universal constraint between efficiency and output power for heat engines operating in the low-dissipation regime. Such a constraint is validated with an example of a Carnot-like engine. Its microscopic dynamics is governed by the master equation. Based on the master equation, we connect the microscopic coupling strengths to the generic parameters in the phenomenological model. We find the usual assumption of low-dissipation is achieved when the coupling to thermal environments is stronger than the driving speed. Additionally, such a connection allows the design of a practical cycle to optimize the engine performance.

The finite-time dynamics, apart from its fundamental importance in nonequilibrium thermodynamics, is of great significance in designing heat engine cycles. We build an experimental apparatus to test the predicted long-time $1/\tau$ scaling of the irreversible entropy generation in the finite-time ($\tau$) thermodynamic process by compressing dry air in a temperature-controlled water bath. We present the first direct experimental validation of the scaling, utilized in many finite-time thermodynamic models at the long-time regime. The experimental data also demonstrate a clear deviation from the scaling at the short-time regime. We show the optimal control scheme to minimize the irreversible entropy generation in finite-time process. Such optimization shall bring new insight to the practical design of heat engine cycles.

Shortcuts to isothermality are driving strategies to steer the system to its equilibrium states within finite time, and enable evaluating the impact of a control promptly. Finding the optimal scheme to minimize the energy cost is of critical importance in applications of this strategy in pharmaceutical drug tests, biological selection, and quantum computation. We prove the equivalence between designing the optimal scheme and finding the geodesic path in the space of control parameters. Such equivalence allows a systematic and universal approach to find the optimal control to reduce the energy cost. We demonstrate the current method with examples of a Brownian particle trapped in controllable harmonic potentials.

To optimize the performance of a heat engine in a finite-time cycle, it is important to understand the finite-time effect of thermodynamic processes. Previously, we have shown that extra work is needed to complete a quantum adiabatic process in finite time, and proved that the extra work follows a $\mathcal{C}/{\tau }^2$ scaling for long control time $\tau$. There the oscillating part of the extra work is neglected due to the complex energy-level structure of the particular quantum system. However, such oscillation of the extra work cannot be neglected in some quantum systems with simple energy-level structure, e.g., the two-level system or the quantum harmonic oscillator. In this paper, we build the finite-time quantum Otto engine on these simple systems, and find that the oscillating extra work leads to a jagged edge in the constraint relation between the output power and the efficiency. By optimizing the control time of the adiabatic processes, the oscillation in the extra work is utilized to enhance the maximum power and the efficiency. We further design special control schemes with the zero extra work at the specific control time. Compared to the linear control scheme, these special control schemes of the finite-time adiabatic process improve the maximum power and the efficiency of the finite-time Otto engine.