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Register a new userThe uniqueness of the integration factor associated with the exchanged heat in thermodynamics
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State functions play important roles in thermodynamics. Different from the process function, such as the exchanged heat $delta Q$ and the applied work $delta W$, the change of the state function can be expressed as an exact differential. We prove here that, for a generic thermodynamic system, only the inverse of the temperature, namely $1/T$, can serve as the integration factor for the exchanged heat $delta Q$. The uniqueness of the integration factor invalidates any attempt to define other state functions associated with the exchanged heat, and in turn, reveals the incorrectness of defining the entransy $E_{vh}=C_VT^2 /2$ as a state function by treating $T$ as an integration factor. We further show the errors in the derivation of entransy by treating the heat capacity $C_V$ as a temperature-independent constant.
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The statistics of the heat exchanged between two quantum XX spin chains prepared at different temperatures is studied within the assumption of weak coupling. This provides simple formulas for the average heat and its corresponding characteristic function, from which the probability distribu- tion may be computed numerically. These formulas are valid for arbitrary sizes and therefore allow us to analyze the role of the thermodynamic limit in this non-equilibrium setting. It is found that all thermodynamic quantities are extremely sensitive to the quantum phase transition of the XX chain.
The second law of thermodynamics can be described as the non-decreasing of the entropy in the irreversible thermodynamic process. Such phenomenon can be quantitatively evaluated with the irreversible entropy generation (IEG), which was recently found to follow a $1/tau$ scaling for the system under a long contact time $tau$ with the thermal bath. This scaling, predicted in many finite-time thermodynamic models, is of great potential in the optimization of heat engines, yet remains lack of direct experimental validation. In this letter, we design an experimental apparatus to test such scaling by compressing dry air in a temperature-controlled water bath. More importantly, we quantitatively verify the optimized control protocol to reduce the IEG. Such optimization shall bring new insight to the practical design of heat engine cycles.
We show that systems with negative specific heat can violate the zeroth law of thermodynamics. By both numerical simulations and by using exact expressions for free energy and microcanonical entropy it is shown that if two systems with the same intensive parameters but with negative specific heat are thermally coupled, they undergo a process in which the total entropy increases irreversibly. The final equilibrium is such that two phases appear, that is, the subsystems have different magnetizations and internal energies at temperatures which are equal in both systems, but that can be different from the initial temperature.
The uniqueness issue of SDE decomposition theory proposed by Ao and his co-workers has recently been discussed. A comprehensive study to investigate connections among different landscape theories [J. Chem. Phys. 144, 094109 (2016)] has pointed out that the decomposition is generally not unique, while Ao et al. (arXiv:1603.07927v1) argues that such conclusions are incorrect because of the missing boundary conditions. In this comment, we will combine literatures research and concrete examples to show that the concrete and effective boundary conditions have not been proposed to guarantee the uniqueness, hence the arguments in [arXiv:1603.07927v1] are not sufficient. Moreover, we show that the uniqueness of the O-U process decomposition referred by YTA paper is unable to serve as a counterexample to ZLs result since additional assumptions have been made implicitly beyond the original SDE decomposition framework, which cannot be applied to general nonlinear cases. Some other issues such as the failure of gradient expansion method will also be discussed. Our demonstration contributes to better understanding of the relevant papers as well as the SDE decomposition theory.
We present the closed loop approach to linear nonequilibrium thermodynamics considering a generic heat engine dissipatively connected to two temperature baths. The system is usually quite generally characterized by two parameters: the output power $P$ and the conversion efficiency $eta$, to which we add a third one, the working frequency $omega$. We establish that a detailed understanding of the effects of the dissipative coupling on the energy conversion process, necessitates the knowledge of only two quantities: the systems feedback factor $beta$ and its open-loop gain $A_{0}$, the product of which, $A_{0}beta$, characterizes the interplay between the efficiency, the output power and the operating rate of the system. By placing thermodynamics analysis on a higher level of abstraction, the feedback loop approach provides a versatile and economical, hence a very efficient, tool for the study of emph{any} conversion engine operation for which a feedback factor may be defined.
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