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Even though irreversibility is one of the major hallmarks of any real life process, an actual understanding of irreversible processes remains still mostly semiempirical. In this paper we formulate a thermodynamic uncertainty principle for irreversible heat engines operating with an ideal gas as a working medium. In particular, we show that the time needed to run through such an irreversible cycle multiplied by the irreversible work lost in the cycle, is bounded from below by an irreducible and process-dependent constant that has the dimension of an action. The constant in question depends on a typical scale of the process and becomes comparable to Plancks constant at the length scale of the order Bohr-radius, i.e., the scale that corresponds to the smallest distance on which the ideal gas paradigm realistically applies.
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The aim of this paper is to determine lost works in a molecular engine and compare results with macro (classical) heat engines. Firstly, irreversible thermodynamics are reviewed for macro and molecular cycles. Secondly, irreversible thermodynamics approaches are applied for a quantum heat engine with -1/2 spin system. Finally, lost works are determined for considered system and results show that macro and molecular heat engines obey same limitations. Moreover, a quantum thermodynamic approach is suggested in order to explain the results previously obtained from an atomic viewpoint.
Brownian heat engines use local temperature gradients in asymmetric potentials to move particles against an external force. The energy efficiency of such machines is generally limited by irreversible heat flow carried by particles that make contact with different heat baths. Here we show that, by using a suitably chosen energy filter, electrons can be transferred reversibly between reservoirs that have different temperatures and electrochemical potentials. We apply this result to propose heat engines based on mesoscopic semiconductor ratchets, which can quasistatically operate arbitrarily close to Carnot efficiency.
A unified $chi$-criterion for heat devices (including heat engines and refrigerators) which is defined as the product of the energy conversion efficiency and the heat absorbed per unit time by the working substance [de Tom{a}s emph{et al} 2012 textit{Phys. Rev. E} textbf{85} 010104(R)] is optimized for tight-coupling heat engines and refrigerators operating between two heat baths at temperatures $T_c$ and $T_h(>T_c)$. By taking a new convention on the thermodynamic flux related to the heat transfer between two baths, we find that for a refrigerator tightly and symmetrically coupled with two heat baths, the coefficient of performance (i.e., the energy conversion efficiency of refrigerators) at maximum $chi$ asymptotically approaches to $sqrt{varepsilon_C}$ when the relative temperature difference between two heat baths $varepsilon_C^{-1}equiv (T_h-T_c)/T_c$ is sufficiently small. Correspondingly, the efficiency at maximum $chi$ (equivalent to maximum power) for a heat engine tightly and symmetrically coupled with two heat baths is proved to be $eta_C/2+eta_C^2/8$ up to the second order term of $eta_Cequiv (T_h-T_c)/T_h$, which reverts to the universal efficiency at maximum power for tight-coupling heat engines operating between two heat baths at small temperature difference in the presence of left-right symmetry [Esposito emph{et al} 2009 textit{Phys. Rev. Lett.} textbf{102} 130602].
Several authors have proposed out of equilibrium thermal engines models, allowing optimization processes involving a trade off between the power output of the engine and its dissipation. These operating regimes are achieved by using objective functions such as the ecological function ($EF$). In order to measure the quality of the balance between these characteristic functions, it was proposed a relationship where power output and dissipation are evaluated in the above mentioned $EF$-regime and they are compared with respect to its values at the regime of maximum power output. We called this relationship Compromise Function and only depends of a parameter that measures the quality of the compromise. Thereafter this function was used to select a value of the mentioned parameter to obtain the generalization of some different objective functions (generalizations of ecological function, omega function and efficient power), by demanding that these generalization parameters maximize the above mentioned functions. In this work we demonstrate that this function can be used directly as an objective function: the $P{Phi}$-Compromise Function ($C_{PPhi}$), also that the operation modes corresponding to the maximum Generalized Ecological Function, maximum Generalized Omega Function and maximum Efficient power output, are special cases of the operation mode of maximum $C_{PPhi}$, having the same optimum high reduced temperature, then the characteristic functions will be the same in any of the above three working regimes, independent of the algebraic complexity of each generalized function. These results are presented for two different models of an irreversible energy converter: a non-endoreversible and a totally irreversible, both with heat leakage.
Typical heat engines exhibit a kind of homotypy: The heat exchanges between a cyclic heat engine and its two heat reservoirs abide by the same function type; the forward and backward flows of an autonomous heat engine also conform to the same function type. This homotypy mathematically reflects in the existence of hidden symmetries for heat engines. The heat exchanges between the cyclic heat engine and its two reservoirs are dual under the joint transformation of parity inversion and time-reversal operation. Similarly, the forward and backward flows in the autonomous heat engine are also dual under the parity inversion. With the consideration of these hidden symmetries, we derive a generic nonlinear constitutive relation up to the quadratic order for tight-coupling cyclic heat engines and that for tight-coupling autonomous heat engines, respectively.
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