We investigate a heat engine with a finite-length Kitaev chain in an ideal Otto cycle. It is found that the critical point of the topological phase transition coincides with the maxima of the efficiency and work output of the total Otto engine. Finite-size effects are taken into account using the method of Hill's nanothermodynamics, as well as using the method of temperature-dependent energy levels. We identify the bulk and boundary thermal cycles of the Kitaev chain engine and find that they are non-ideal Otto cycles. The physics of deviation from ideal Otto cycle is identified as a finite size effect, which we dub as "internal geometric friction", leading to heat transfer from the bulk to the boundary during adiabatic transformation of the whole system. Besides, we determine the regimes allowing for independently running an ideal Otto refrigerator at the boundary and an ideal Otto engines in the bulk and in the whole system. Furthermore, we show that the first-order phase transition in the boundary and the second-order phase transition in the bulk can be identified through their respective contributions to the engine work output.
We investigate a heat engine with a finite length Kitaev chain in an Otto cycle. Finite size effects are taken into account using method of Hill's nano-thermodynamics as well as using the method of temperature dependent energy levels. We distinguish the bulk and boundary contributions to the efficiency and the work output of Kitaev chain engine and identify them as non-Otto heat engine and refrigerator cycles, respectively. Possibility of separately running Otto engine cycles associated with the bulk and the whole system, and an Otto refrigerator at the boundary is pointed out. It is found tha…
In finite-time quantum heat engines, some work is consumed to drive a working fluid accompanying coherence, which is called `friction'. To understand the role of friction in quantum thermodynamics, we present a couple of finite-time quantum Otto cycles with two different baths: Agarwal versus Lindbladian. We solve them exactly and compare the performance of the Agarwal engine with that of the Lindbladian engine. In particular, we find remarkable and counterintuitive results that the performance of the Agarwal engine due to friction can be much higher than that in the quasistatic limit with the…
We consider two spin-1/2 particles with isotropic Heisenberg interaction, as the working substance of a quantum heat engine. We observe a frictional effect on the adiabatic branches of the heat cycle, which arises due to an inhomogeneous driving at a finite rate of the external magnetic field. The frictional effect is characterized by entropy production in the system and reduction in the work extracted. Corresponding to a sudden and a very slow driving, we find expressions for the lower and upper bounds of work that can be extracted on the adiabatic branches. These bounds are also confirmed wi…
We explore the transport features of a Brownian particle that walks in a periodic ratchet potential that is coupled with a spatially varying temperature background. Since the viscous friction of the medium decreases as the temperature of the medium increases, any reasonable exploration regarding the thermodynamic features of the Brownian engine should take into account the role of temperature on the viscosity of the fluid. In this work, we study this effect of temperature by considering a viscous friction that decreases exponentially as the background temperature increases. Our result depicts …
The operation of a quantum heat engine in finite time generally faces a trade-off between efficiency and power. Using shortcuts to adiabaticity (STA), this trade off can be avoided to engineer thermal machines that operate at maximum efficiency and tunable output power. We demonstrate the use of STA to engineer a scalable superadiabatic quantum Otto cycle and report recent experimental progress to tailor quantum friction in finite-time quantum thermodynamics. In the presence of quantum friction, it is also shown that the use of a many-particle working medium can boost the performance of the qu…
The reversible nature of thermodynamical cycles is an idealisation based on the assumption of perfect quasi-static dynamics. As a consequence of this assumption, ideal engines operate at the maximum efficiency but have zero power. Realistic engines, on the other hand, operate in finite-time and are intrinsically irreversible, implying friction effects at short cycle times. The engineering goal is to find the maximum efficiency allowed at the maximum possible power. In the current technological age, with our ability to manipulate devices at the nanoscale and beyond, one must understand the cons…
We examine a quantum heat engine with an interacting many-body working medium consisting of the long-range Kitaev chain to explore the role of long-range interactions in the performance of the quantum engine. By analytically studying two type of thermodynamic cycles, namely Otto cycle and Stirling cycle, we demonstrate that the work output and efficiency of long-range interacting heat engine can be boosted by long-range interactions, in comparison to the short-range counterpart. We further show that in the Otto cycle, there exist an optimal condition for which the largest enhancement of work o…
A colloidal particle embedded in a fluid can be used as a microscopic heat engine by means of a sequence of cyclic transformations imposed by an optical trap. We investigate a model for the operation of such kind of Brownian engines when the surrounding medium is viscoelastic, which endows the particle dynamics with memory friction. We analyze the effect of the relaxation time of the fluid on the performance of the colloidal engine under finite-time Stirling cycles. We find that, due to the frequency-dependence of the friction in viscoelastic fluids, the mean power delivered by the engine and …
We consider a finite-time Otto engine operating on a quantum harmonic oscillator and driven by shortcut-to-adiabaticity (STA) techniques to speed up its cycle. We study its efficiency and power when internal friction, time-averaged work, and work fluctuations are used as quantitative figures of merit, showing that time-averaged efficiency and power are useful cost functions for the characterization of the performance of the engine. We then use the minimum allowed time for validity of STA protocol relation to establish a physically relevant bound to the efficiency at maximum power of the STA-dr…
The Kitaev model on the honeycomb lattice is a paradigmatic system known to host a wealth of nontrivial topological phases and Majorana edge modes. In the static case, the Majorana edge modes are nondispersive. When the system is periodically driven in time, such edge modes can disperse and become chiral. We obtain the full phase diagram of the driven model as a function of the coupling and the driving period. We characterize the quantum criticality of the different topological phase transitions in both the static and driven model via the notions of Majorana-Wannier state correlation functions…
We show that finite system-reservoir coupling imposes a distinct quantum limit on the performance of a non-equilibrium quantum heat engine. Even in the absence of quantum friction along the isentropic strokes, finite system-reservoir coupling induces correlations that result in the generation of coherence between the energy eigenstates of the working system. This coherence acts to hamper the engine's power output, as well as the efficiency with which it can convert heat into useful work, and cannot be captured by a standard Born-Markov analysis of the system-reservoir interactions.
We investigate the efficiency at maximum power of an irreversible Carnot engine performing finite-time cycles between two reservoirs at temperatures $T_h$ and $T_c$ $(T_c<T_h)$, taking into account of internally dissipative friction in two "adiabatic" processes. In the frictionless case, the efficiencies at maximum power output are retrieved to be situated between $η_{_C}/$ and $η_{_C}/(2-η_{_C})$, with $η_{_C}=1-T_c/{T_h}$ being the Carnot efficiency. The strong limits of the dissipations in the hot and cold isothermal processes lead to the result that the efficiency at maximum power output a…
We study the efficiency at maximum power of non-adiabatic dissipative (internally dissipative friction in finite time adiabatic processes) Carnot-like heat engines operate in finite time under the power law dissipation regime. We find that the non-adiabatic dissipation does not influence the universal minimum and maximum bounds on the efficiency at maximum power obtained in the generalized dissipative Carnot-like heat engines which does not take in to account the non-adiabatic dissipation.
We propose a novel type of quantum heat engine based on the ultrafast dynamical control of the magnetic properties of a nano-scale working body. The working principle relies on nonlinear phononics, an example for dynamical materials design. We describe the general recipe for identifying candidate materials, and also propose Cr$_{2}$O$_{3}$ as a promising working body for a quantum Otto cycle. Using a spin Hamiltonian as a model for Cr$_{2}$O$_{3}$, we investigate the performance in terms of efficiency, output power, and quantum friction. To assess the assumptions underlying our effective spin …
We propose a simple mechanical model of locomotion induced by internal force and friction. We first construct a system of two elements as an analog of the bipedal motion. The internal force does not induce a directional motion by itself because of the action-reaction law, but a directional motion becomes possible by the control of the frictional force. The efficiency of these model systems is studied using an analogy to the heat engine. As a modified version of the two-elements model, we construct a model which exhibits a bipedal motion similar to kinesin's motion of molecular motor. Next, we …
A dynamical model of a highly efficient heat engine is proposed, where an applied temperature difference maintains the motion of particles around the circuit consisting of two asymmetric narrow channels, in one of which the current flows against the applied thermodynamic forces. Numerical simulations and linear-response analysis suggest that, in the absence of frictional losses, the Carnot efficiency can be achieved in the thermodynamic limit.
We study thermodynamic processes in contact with a heat bath that may have an arbitrary time-varying periodic temperature profile. Within the framework of stochastic thermodynamics, and for models of thermo-dynamic engines in the idealized case of underdamped particles in the low-friction regime, we derive explicit bounds as well as optimal control protocols that draw maximum power and achieve maximum efficiency at any specified level of power.
