In existing linear response theories for adiabatically driven cyclic heat engines, Onsager symmetry is identified only phenomenologically, and a relation between global and local Onsager coefficients, defined over one cycle and at any instant of a cycle, respectively, is not derived. To address this limitation, we develop a linear response theory for the speed of adiabatically changing parameters and temperature differences in generic Gaussian heat engines obeying Fokker--Planck dynamics. We establish a hierarchical relationship between the global linear response relations, defined over one cycle of the heat engines, and the local ones, defined at any instant of the cycle. This yields a detailed expression for the global Onsager coefficients in terms of the local Onsager coefficients. Moreover, we derive an efficiency bound, which is tighter than the Carnot bound, for adiabatically driven linear irreversible heat engines based on the detailed global Onsager coefficients. Finally, we demonstrate the application of the theory using the simplest stochastic Brownian heat engine model.
In the recent progress in nonequilibrium thermodynamics, information has been recognized as a kind of thermodynamic resource that can drive thermodynamic current without any direct energy injection. In this paper, we establish the framework of linear irreversible thermodynamics for a broad class of autonomous information processing. In particular, we prove that the Onsager reciprocity holds true with information: The linear response matrix is well-defined, and is shown symmetric with both of the information affinity and the conventional thermodynamic affinity. As an application, we derive a un…
We apply the model of minimally nonlinear irreversible heat engines developed by Izumida and Okuda [EPL {\bf 97}, 10004 (2012)] to refrigerators. The model assumes extended Onsager relations including a new nonlinear term accounting for dissipation effects. The bounds for the optimized regime under an appropriate figure of merit and the tight-coupling condition are analyzed and successfully compared with those obtained previously for low-dissipation Carnot refrigerators in the finite-time thermodynamics framework. Besides, we study the bounds for the nontight-coupling case numerically. We also…
The performance of a generic, cyclic heat engine between two heat reservoirs is discussed within a linear-irreversible framework. The Onsager reciprocal relation is derived as a consequence of the equivalence between quasi-static and reversible operations, under the tight-coupling condition. When the latter condition is relaxed, it is possible to achieve reversible cycle in a finite duration. Onsager reciprocity must be violated when either the quasi-static cycle is not reversible, or the reversible cycle is not quasi-static.
It is shown that Onsager's principle of the least dissipation of energy is equivalent to the maximum entropy production principle. It is known that solutions of the linearized Boltzmann equation make extrema of entropy production. It is argued, in the case of stationary processes, that this extremum is a maximum rather than a minimum.
We study a Brownian Carnot cycle introduced by T. Schmiedl and U. Seifert [Europhys. Lett. \textbf{81}, 20003 (2008)] from a viewpoint of the linear irreversible thermodynamics. By considering the entropy production rate of this cycle, we can determine thermodynamic forces and fluxes of the cycle and calculate the Onsager coefficients for general protocols, that is, arbitrary schedules to change the potential confining the Brownian particle. We show that these Onsager coefficients contain the information of the protocol shape and they satisfy the tight-coupling condition irrespective of whatev…
Building on our earlier work (Proesmans et. al., Phys.~Rev.~X \textbf{6} (2016), 041010), we introduce the underdamped Brownian duet as a prototype model of a dissipative system or of a work-to-work engine. Several recent advances from the theory of stochastic thermodynamics are illustrated with explicit analytic calculations and corresponding Langevin simulations. In particular, we discuss Onsager-Casimir symmetry, the trade-off relations between power, efficiency and dissipation, and stochastic efficiency.
Low-temperature-differential (LTD) Stirling heat engines are able to operate with a small temperature difference between low-temperature heat reservoirs that exist in our daily lives, and thus they are considered to be an important sustainable energy technology. The author recently proposed a nonlinear dynamics model of an LTD kinematic Stirling heat engine to study the rotational mechanism of the engine [Y. Izumida, EPL \textbf{121}, 50004 (2018)]. This paper presents our study of the nonequilibrium thermodynamics analysis of this engine model, where a load torque against which the engine doe…
The diffusive motion of colloidal particles dispersed in a premelting solid is analyzed within the framework of irreversible thermodynamics. We determine the mass diffusion coefficient, thermal diffusion coefficient and Soret coefficient of the particles in the dilute limit, and find good agreement with experimental data. In contrast to liquid suspensions, the unique nature of premelting solids allows us to derive an expression for the Dufour coefficient and independently verify the Onsager reciprocal relation coupling diffusion to the flow of heat.
We propose the minimally nonlinear irreversible heat engine as a new general theoretical model to study the efficiency at the maximum power $η^*$ of heat engines operating between the hot heat reservoir at the temperature $T_h$ and the cold one at $T_c$ ($T_c \le T_h $). Our model is based on the extended Onsager relations with a new nonlinear term meaning the power dissipation. In this model, we show that $η^*$ is bounded from the upper side by a function of the Carnot efficiency $η_C\equiv 1-T_c/T_h$ as $η^*\le η_C/(2-η_C)$. We demonstrate the validity of our theory by showing that the low-d…
We formulate an endoreversible finite-time Carnot cycle model based on the assumptions of local equilibrium and constant energy flux, where the efficiency and the power are expressed in terms of the thermodynamic variables of the working substance. By analyzing the entropy production rate caused by the heat transfer in each isothermal process during the cycle, and using an endoreversible condition applied to the linear response regime, we identify the thermodynamic flux and force of the present system and obtain a linear relation that connects them. We calculate the efficiency at maximum power…
Thermoelectricity is traditionally explained via Onsager's irreversible, flux-force framework. The coupled flows of heat and electric charge are modelled as steady-state flows, driven by the thermodynamic forces defined in terms of the gradients of local, intensive parameters like temperature and electrochemical potential. A thermoelectric generator is a device with a finite extension, and its performance is measured in terms of total power output and total entropy generation. These global quantities are naturally expressed in terms of discrete or global forces derived from their local counter…
We consider the efficiency at maximum power of a quantum Otto engine, which uses a spin or a harmonic system as its working substance and works between two heat reservoirs at constant temperatures $T_h$ and $T_c$ $ (<T_h)$. Although the spin-$1/2$ system behaves quite differently from the harmonic system in that they obey two typical quantum statistics, the efficiencies at maximum power based on these two different kinds of quantum systems are bounded from the upper side by the same expression of the efficiency at maximum power: $η_{mp}\leqη_+\equiv η_C^2/[η_C-(1-η_C)\ln(1-η_C)]$, with $η_C=1-…
The impossibility of attaining equilibrium for cyclic chemical reaction networks with irreversible steps is apparently due to a divergent entropy production rate. A deeper reason seems to be the violation of the detailed balance condition. In this work, we discuss how the standard theoretical framework can be adapted to include irreversible cycles, avoiding the divergence. With properly redefined force terms, such systems are also seen to reach and sustain equilibria that are characterized by the vanishing of the entropy production rate, though detailed balance is not maintained. Equivalence o…
We study the energetics of isothermal ratchets which are driven by a chemical reaction between two states and operate in contact with a single heat bath of constant temperature. We discuss generic aspects of energy transduction such as Onsager relations in the linear response regime as well as the efficiency and dissipation close to and far from equilibrium. In the linear response regime where the system operates reversibly the efficiency is in general nonzero. Studying the properties for specific examples of energy landscapes and transitions, we observe in the linear response regime that the …
Building on a model introduced by Mandal and Jarzynski [Proc. Natl. Acad. Sci. U. S. A., {\bf 109}, (2012) 11641], we present a simple version of an autonomous reversible Maxwell's demon. By changing the entropy of a tape consisting of a sequence of bits passing through the demon, the demon can lift a mass using the coupling to a heat bath. Our model becomes reversible by allowing the tape to move in both directions. In this thermodynamically consistent model, total entropy production consists of three terms one of which recovers the irreversible limit studied by MJ. Our demon allows an interp…
We present an in-depth analysis of the sometimes understated role of the principle of energy conservation in linear irreversible thermodynamics. Our case study is that of a thermoelectric generator (TEG), which is a heat engine of choice in irreversible thermodynamics, owing to the coupling between the electrical and heat fluxes. We show why Onsager's reciprocal relations must be considered locally and how internal dissipative processes emerge from the extension of these relations to a global scale: the linear behavior of a heat engine at the local scale is associated with a dissipation proces…
