Abstract
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.
Highlights
The Carnot efficiency is the fundamental bound for the efficiency of heat engines, and it is universally imposed by equilibrium thermodynamics [1]
We focus on the simplest heat engine model
Equation (32) constitutes our second main result. It yields a tighter bound than the Carnot efficiency imposed by the conventional second law of thermodynamics and is attained for an optimal protocol under a given cycle speed
Summary
The Carnot efficiency is the fundamental bound for the efficiency of heat engines, and it is universally imposed by equilibrium thermodynamics [1]. The application of linear irreversible thermodynamics to heat engines operating under small temperature differences has been limited, until recently [30,31,32,33,34,35,36,37,38] This is because the identification of thermodynamic fluxes and forces is highly complex for heat engines undergoing cyclic changes. The Onsager coefficients defined globally for a one-cycle period of ac driving, which determine the overall performance of the thermoelectrics, are expressed in terms of locally defined Onsager coefficients at any instant during driving [40,41] The key of this formulation is to apply the standard linear response theory to instantaneous equilibrium states specified by the adiabatically changing parameters that are regarded to have “frozen,” fixed values. Based on the detailed structure of the Onsager coefficients, we derive an efficiency
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