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SCIENCE CHINA Technological Sciences, Volume 60 , Issue 3 : 363-373(2017) https://doi.org/10.1007/s11431-016-0624-1

Discussion on the extensions of the entransy theory

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  • ReceivedAug 22, 2016
  • AcceptedNov 24, 2016
  • PublishedJan 17, 2017

Abstract

In this paper, the preconditions for the extensions of the entransy theory are summarized and discussed. As the physical meaning of entransy is the “potential energy” of thermal energy, the concepts and analyses method of the entransy theory can be extended based on the viewpoint of potential energy. The extension to microeconomics is taken as an example to show how the entransy theory is extended. The concept of economic entransy is defined based on the analogy analysis between heat transfer and microeconomics, and the indirect tax is found to be the “potential energy” of goods or services that the government takes from the market. With the extension, a new viewpoint is introduced to understand and analyze the microeconomic system. If the irreversibility in nature makes the potential energy in one system can never increase automatically, the entransy decrease principle and the corresponding equilibrium criteria can further be extended. Furthermore, if the mathematical expressions of the governing equations of the analyzed physical or social phenomena in the system are the same as those in heat transfer, the principle of least action and the optimization principles in the entransy theory can be extended. More similarities between heat transfer and the other phenomena result in more extensions of the entransy theory.


Funded by

Science Fund for Creative Research Groups(51321002)

National Natural Science Foundation of China(51376101 & 51356001)


Acknowledgment

This work was supported by the National Natural Science Foundation of China (Grant Nos. 51376101 & 51356001), and the Science Fund for Creative Research Groups (Grant No. 51321002).


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  • Figure 1

    (Color online) A one-dimensional heat transfer system and a simple microeconomic system. (a) A one-dimensional heat transfer system; (b) a simple microeconomic system.

  • Figure 2

    (Color online) The sketch of T-Q diagram of the device.

  • Figure 3

    (Color online) Variations of Gdis-d with Qd for different values of kH and kL.

  • Figure 4

    (Color online) The sketch of P-N diagram of the market.

  • Figure 5

    (Color online) Variations of GV-m with Nm for different values of mH and mL.

  • Figure 6

    (Color online) The sketch of P-N diagram for different value of mH and mL.

  • Figure 7

    (Color online) Variations of the maximum GV-m and the optimal Nm with mL.

  • Figure 8

    (Color online) Variations of the maximum GV-m and the optimal Nm with mH.

  • Figure 9

    (Color online) The sketch of P-N diagram when the indirect tax is negative.

  • Table 1   Some potential energies in nature and their corresponding conservative extensive and intensive quantities

    Potential energy

    Conservative extensive quantity

    Intensive quantity

    Geopotential energy

    mass

    gravity potential

    Electrostatic potential energy

    electrical charge

    electrical potential

    Chemical potential energy

    chemical potential

    amount of substance

    Entransy [2,3]

    thermal energy

    temperature

    Mass entransy [4,37]

    component mass

    component concentration

    Momentum entransy [35,37]

    momentum

    velocity

    Radiative entransy [12]

    thermal energy

    radiative thermal potential

  • Table 2   Analogy between heat transfer and microeconomics

    Parameters

    Heat transfer

    Microeconomics

    Conservative intensive quantity

    heat

    quantity of goods or services

    Potential (intensive quantity)

    temperature

    price

    Flow of conservative intensive quantity

    heat flow

    flow of goods or services

    Driven force

    temperature difference

    price difference

    Potential energy (nonconservation)

    entransy

    economic entransy (nominal value)

    Flow of nonconservative intensive quantity

    entransy flow

    economic entransy flow

    (money flow)

    Variation of potential energy

    entransy dissipation

    economic entransy variation (indirect tax)

    Diagram

    T-Q diagram

    P-N diagram

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