Skip to main content
Log in

Entransy: its physical basis, applications and limitations

  • Review
  • Engineering Thermophysics
  • Published:
Chinese Science Bulletin

Abstract

In this paper, the physical basis and application conditions of the entransy theory are reviewed and discussed. Entransy can be obtained from the analogy between heat and electrical conductions. It is a state value and the “potential energy” of heat. From the viewpoint of thermomass, it reflects the thermal energy of the thermomass in an object. Furthermore, it was also related to the microstate number and is a single value function of the microstate number. The concepts of entransy, entransy flux and entransy dissipation can be used to express the least action of heat transfer. The entransy balance equations for heat transfer and thermodynamic processes and their applications to thermal systems are also reviewed. The differences between the entransy theory, constructal theory, entropy generation minimization, exergy analyses method, principle of uniformity of temperature difference field and field synergy (coordination) principle are also discussed. The entransy theory is different from the other discussed theories. The limitations of the entransy theory are also discussed.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Subscribe and save

Springer+
from $39.99 /Month
  • Starting from 10 chapters or articles per month
  • Access and download chapters and articles from more than 300k books and 2,500 journals
  • Cancel anytime
View plans

Buy Now

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Fig. 1
Fig. 2

Similar content being viewed by others

References

  1. Guo ZY, Zhu HY, Liang XG (2007) Entransy—a physical quantity describing heat transfer ability. Int J Heat Mass Transfer 50:2545–2556

    Google Scholar 

  2. Bergles AE (1981) Application of heat transfer augmentation. Hemisphere, Washington, DC

    Google Scholar 

  3. Gupta JP (1985) Fundamentals of heat exchanger and pressure vessel technology. Hemisphere, Washington, DC

    Google Scholar 

  4. Webb RL (1995) Principles of enhanced heat transfer. Hemisphere, Washington, DC

    Google Scholar 

  5. Bejan A (1997) Advanced engineering thermodynamics, 2nd edn. Wiley, New York

    Google Scholar 

  6. David B, Ramousse J, Luo L (2012) Optimization of thermoelectric heat pumps by operating condition management and heat exchanger design. Energy Convers Manag 60:125–133

    Google Scholar 

  7. Shah RK, Skiepko T (2004) Entropy generation extrema and their relationship with heat exchanger effectiveness—number of transfer unit behavior for complex flow arrangements. J Heat Transf 126:994–1002

    Google Scholar 

  8. Guo ZY, Li ZX, Zhou SQ (1996) Principle of uniformity of temperature difference field in heat exchanger. Sci China Ser E Technol Sci 39:68–75

    Google Scholar 

  9. Guo ZY, Tao WQ, Shah RK (2005) The field synergy (coordination) principle and its applications in enhancing single phase convective heat transfer. Int J Heat Mass Transf 48:1797–1807

    Google Scholar 

  10. Chen Q, Zhu HY, Pan N et al (2011) An alternative criterion in heat transfer optimization. Proc R Soc A Math Phys 467:1012–1028

    Google Scholar 

  11. Chen LG (2012) Progress in entransy theory and its applications. Chin Sci Bull 57:4404–4426

    Google Scholar 

  12. Chen LG, Xiao QH, Xie ZH et al (2013) Constructal entransy dissipation rate minimization for tree-shaped assembly of fins. Int J Heat Mass Transf 67:506–513

    Google Scholar 

  13. Chen LG, Xiao QH, Xie ZH et al (2012) T-shaped assembly of fins with constructal entransy dissipation rate minimization. Int Commun Heat Mass Transf 39:1556–1562

    Google Scholar 

  14. Feng HJ, Chen LG, Xie ZH et al (2013) Constructal optimization for H-shaped multi-scale heat exchanger based on entransy theory. Sci China Technol Sci 56:299–307

    Google Scholar 

  15. Chen L, Wei S, Sun F (2011) Constructal entransy dissipation rate minimization of a disc. Int J Heat Mass Transf 54:210–216

    Google Scholar 

  16. Wei S, Chen L, Sun F (2011) Constructal entransy dissipation rate minimization of round tube heat exchanger cross-section. Int J Therm Sci 50:1285–1292

    Google Scholar 

  17. Yuan F, Chen Q (2011) Two energy conservation principles in convective heat transfer optimization. Energy 36:5476–5485

    Google Scholar 

  18. Liu W, Liu ZC, Jia H et al (2011) Entransy expression of the second law of thermodynamics and its application to optimization in heat transfer process. Int J Heat Mass Transf 54:3049–3059

    Google Scholar 

  19. Cheng XT, Liang XG (2011) Entransy flux of thermal radiation and its application to enclosures with opaque surfaces. Int J Heat Mass Transf 54:269–278

    Google Scholar 

  20. Cheng XT, Xu XH, Liang XG (2011) Radiative entransy flux in enclosures with non-isothermal or non-grey, opaque, diffuse surfaces and its application. Sci China Technol Sci 54:2446–2456

    Google Scholar 

  21. Guo ZY, Liu XB, Tao WQ et al (2010) Effectiveness-thermal resistance method for heat exchanger design and analysis. Int J Heat Mass Transf 53:2877–2884

    Google Scholar 

  22. Cheng XT, Zhang QZ, Liang XG (2012) Analyses of entransy dissipation, entropy generation and entransy-dissipation-based thermal resistance on heat exchanger optimization. Appl Therm Eng 38:31–39

    Google Scholar 

  23. Cheng XT, Liang XG (2012) Computation of effectiveness of two-stream heat exchanger networks based on concepts of entropy generation, entransy dissipation and entransy-dissipation-based thermal resistance. Energy Convers Manag 58:163–170

    Google Scholar 

  24. Cheng XT, Liang XG (2012) Optimization principles for two-stream heat exchangers and two-stream heat exchanger networks. Energy 46:386–392

    Google Scholar 

  25. Cheng XT, Liang XG, Guo ZY (2011) Entransy decrease principle of heat transfer in an isolated system. Chin Sci Bull 56:847–854

    Google Scholar 

  26. Xu MT (2011) The thermodynamic basis of entransy and entransy dissipation. Energy 36:4272–4277

    Google Scholar 

  27. Xu MT (2012) Variational principles in terms of entransy for heat transfer. Energy 44:973–977

    Google Scholar 

  28. Li XF, Guo JF, Xu MT et al (2011) Entransy dissipation minimization for optimization of heat exchanger design. Chin Sci Bull 56:2174–2178

    Google Scholar 

  29. Qian XD, Li ZX (2011) Analysis of entransy dissipation in heat exchangers. Int J Therm Sci 50:608–614

    Google Scholar 

  30. Cheng XT, Liang XG (2012) Entransy loss in thermodynamic processes and its application. Energy 44:964–972

    Google Scholar 

  31. Cheng XT, Wang WH, Liang XG (2012) Optimization of heat transfer and heat-work conversion based on generalized heat transfer law. Sci China Technol Sci 55:2847–2855

    Google Scholar 

  32. Cheng XT, Liang XG (2012) Heat-work conversion optimization of one-stream heat exchanger networks. Energy 47:421–429

    Google Scholar 

  33. Cheng XT, Chen Q, Hu GJ et al (2013) Entransy balance for the closed system undergoing thermodynamic processes. Int J Heat Mass Transf 60:180–187

    Google Scholar 

  34. Cheng XT, Liang XG (2013) Discussion on the entransy expressions of the laws of thermodynamics and their applications. Energy 56:46–51

    Google Scholar 

  35. Cheng XT, Liang XG (2013) Entransy, entransy dissipation and entransy loss for analyses of heat transfer and heat–work conversion processes. J Therm Sci Technol 8:337–352

    Google Scholar 

  36. Cheng XT, Liang XG (2013) Analyses and optimizations of thermodynamic performance of an air conditioning system for room heating. Energy Build 67:387–391

    Google Scholar 

  37. Wang WH, Cheng XT, Liang XG (2013) Entropy and entransy analyses and optimizations of the Rankine cycle. Energy Convers Manag 68:82–88

    Google Scholar 

  38. Cheng XT, Liang XG (2013) Entransy and entropy analyses of heat pump systems. Chin Sci Bull 58:4696–4702

    Google Scholar 

  39. Cheng XT, Liang XG (2014) Discussion on the applicability of entropy generation minimization and entransy theory to the evaluation of thermodynamic performance for heat pump systems. Energy Convers Manag 80:238–242

    Google Scholar 

  40. Guo ZY, Cheng XG, Xia ZZ (2003) Least dissipation principle of heat transport potential capacity and its application in heat conduction optimization. Chin Sci Bull 48:406–410

    Google Scholar 

  41. Cheng XG, Li ZX, Guo ZY (2003) Heat conduction optimization based on least dissipation principle of heat transport potential capacity. J Eng Thermophys 24:94–96 (in Chinese)

    Google Scholar 

  42. Cheng XG, Meng JA, Guo ZY (2005) Potential capacity dissipation minimization and entropy generation minimization in heat conduction optimization. J Eng Thermophys 26:1034–1036 (in Chinese)

    Google Scholar 

  43. Han GZ, Guo ZY (2006) Two different thermal optimization objective functions: dissipation of heat transport potential capacity and entropy production. J Eng Thermophys 27:811–813 (in Chinese)

    Google Scholar 

  44. Wu J, Cheng XG, Meng JA et al (2006) Potential capacity dissipation extremum and entropy generation minimization in laminar convective heat transfer. J Eng Thermophys 27:100–102 (in Chinese)

    Google Scholar 

  45. Wei Q (2008) Bounds on dissipation of heat transport potential capacity in turbulent convection with volume heat source. J Eng Thermophys 29:1354–1356 (in Chinese)

    Google Scholar 

  46. Schneider PJ (1955) Conduction heat transfer. Addison-Wesley, Reading, pp 338–339

    Google Scholar 

  47. Hu GJ, Cao BY, Guo ZY (2011) Entransy and entropy revisited. Chin Sci Bull 56:2974–2977

    Google Scholar 

  48. Cheng XT, Dong Y, Liang XG (2011) Potential entransy and potential entransy decrease principle. Acta Phys Sin 60:114402 (in Chinese)

    Google Scholar 

  49. Cao BY, Guo ZY (2007) Equation of motion of a phonon gas and non-Fourier heat conduction. J Appl Phys 102:053503

    Google Scholar 

  50. Dong Y, Cao BY, Guo ZY (2011) Generalized heat conduction laws based on thermomass theory and phonon hydrodynamics. J Appl Phys 110:063504

    Google Scholar 

  51. Wang HD, Cao BY, Guo ZY (2010) Heat flow choking in carbon nanotubes. Int J Heat Mass Transfer 53:1796–1800

    Google Scholar 

  52. Guo ZY, Cao BY, Zhu HY et al (2007) State equation of phonon gas and conservation equations for phonon gas motion. Acta Phys Sin 56:3306–3312 (in Chinese)

    Google Scholar 

  53. Huang K (2009) Solid state physics. Peking University Press, Beijing (in Chinese)

  54. Cheng XT, Liang XG (2013) From thermomass to entransy. Int J Heat Mass Transf 62:174–177

    Google Scholar 

  55. Cheng XT, Liang XG, Xu XH (2011) Microscopic expression of entransy. Acta Phys Sin 60:060512 (in Chinese)

    Google Scholar 

  56. Tien CL, Lienhard JH (1987) The statistical thermodynamics. Tsinghua University Press, Beijing, pp 148–182 (in Chinese)

    Google Scholar 

  57. Feng D, Feng ST (2005) The world of entropy. Science Press, Beijing (in Chinese)

    Google Scholar 

  58. Zhu WH, Gu YQ (1983) The basic statistical physics. Tsinghua University Press, Beijing, pp 153–194 (in Chinese)

    Google Scholar 

  59. Cheng XG (2004) Entransy and its application in heat transfer optimization. Dissertation of doctoral degree, Tsinghua University, Beijing (in Chinese)

  60. Lu MW, Luo XF (2001) Basic elastic theory. Tsinghua University Press, Beijing (in Chinese)

    Google Scholar 

  61. Cheng XG, Li ZX, Guo ZY (2004) Variational principles in heat conduction. J Eng Thermophys 25:457–459 (in Chinese)

    Google Scholar 

  62. Cheng XT, Liang XG, Xu XH (2011) Principles of potential entransy in generalized flow. Acta Phys Sin 60:118103 (in Chinese)

    Google Scholar 

  63. Chen Q, Ren JX (2008) Generalized thermal resistance for convective heat transfer and its relation to entransy dissipation. Chin Sci Bull 53:3753–3761

    Google Scholar 

  64. Xia SJ, Chen LG, Sun FR (2010) Optimal paths for minimizing entransy dissipation during heat transfer processes with generalized radiative heat transfer law. Appl Math Model 34:2242–2255

    Google Scholar 

  65. Xia SJ, Chen LG, Sun FR (2009) Optimization for entransy dissipation minimization in heat exchanger. Chin Sci Bull 54:3587–3595

    Google Scholar 

  66. Zheng ZJ, He YL, Li YS (2014) An entransy dissipation-based optimization principle for solar power tower plants. Sci China Technol Sci 57:773–783

    Google Scholar 

  67. Jia H, Liu ZC, Liu W et al (2014) Convective heat transfer optimization based on minimum entransy dissipation in the circular tube. Int J Heat Mass Transf 73:124–129

    Google Scholar 

  68. Feng HJ, Chen LG, Sun FR (2012) “Volume-point” heat conduction constructal optimization based on entransy dissipation rate minimization with three-dimensional cylindrical element and rectangular and triangular elements at micro and nanoscales. Sci China Technol Sci 55:779–794

    Google Scholar 

  69. Chen L, Feng H, Xie Z et al (2013) Constructal optimization for “disc-point” heat conduction at micro and nanoscales. Int J Heat Mass Transf 67:704–711

    Google Scholar 

  70. Xiao QH, Chen LG, Sun FR (2011) Constructal entransy dissipation rate minimization for “disc-point” heat conduction. Chin Sci Bull 56:102–112

    Google Scholar 

  71. Xiao QH, Chen LG, Sun FR (2011) Constructal entransy dissipation rate minimization for heat conduction based on a tapered element. Chin Sci Bull 56:2400–2410

    Google Scholar 

  72. Wei S, Chen L, Sun F (2010) Constructal entransy dissipation minimization for “volume-point” heat conduction without the premise of optimized last-order construct. Int J Exergy 7:627–639

    Google Scholar 

  73. Feng HJ, Chen LG, Xie ZH et al (2014) Constructal entransy dissipation rate minimization for “volume-point” heat conduction at micro and nanoscales. J Energy Inst (in press). doi:10.1016/j.joei.2014.06.002

  74. Feng HJ, Chen LG, Xie ZH et al (2014) Constructal entransy dissipation rate minimization for variable cross-section insulation layer of the steel rolling reheating furnace wall. Int Commun Heat Mass Transf 52:26–32

    Google Scholar 

  75. Feng HJ, Chen LG, Xie ZH et al (2014) Generalized constructal optimization for secondary cooling process of slab continuous casting based on entransy theory. Sci China Technol Sci 57:784–795

    Google Scholar 

  76. Feng HJ, Chen LG, Xie ZH et al (2014) Constructal entransy optimizations for insulation layer of steel rolling reheating furnace wall with convective and radiative boundary conditions. Chin Sci Bull 59:2470–2477

    Google Scholar 

  77. Xia SJ, Chen LG, Sun FR (2010) Entransy dissipation minimization for liquid-solid phase processes. Sci China Technol Sci 53:960–968

    Google Scholar 

  78. Yang AB, Chen LG, Xia SJ et al (2014) The optimal configuration of reciprocating engine based on maximum entransy loss. Chin Sci Bull 59:2031–2038

    Google Scholar 

  79. Bejan A (1997) Constructal-theory network of conducting paths for cooling a heat generating volume. Int J Heat Mass Transf 40:779–816

    Google Scholar 

  80. Bejan A, Lorente S (2013) Constructal law of design and evolution: Physics, biology, technology, and society. J Appl Phys 113:151301

    Google Scholar 

  81. Chen LG (2012) Progress in study on constructal theory and its applications. Sci China Techol Sci 55:802–820

    Google Scholar 

  82. Feng HJ, Chen LG, Xie ZH et al (2014) Generalized constructal optimization for solidification heat transfer process of slab continuous casting based on heat loss rate. Energy 66:991–998

    Google Scholar 

  83. Wu W, Chen L, Sun F (2007) Heat-conduction optimization based on constructal theory. Appl Energy 84:39–47

    Google Scholar 

  84. Berry RS, Kazakov VA, Sieniutycz S et al (1999) Thermodynamic optimization of finite time processes. Wiley, Chichester

    Google Scholar 

  85. Chen L, Wu C, Sun F (1999) Finite time thermodynamic optimization or entropy generation minimization of energy systems. J Non-Equilib Thermodyn 24:327–359

    Google Scholar 

  86. Bejan A (2014) “Entransy”, and its lack of content in physics. ASME J Heat Transf 136:055501

    Google Scholar 

  87. Bejan A, Lorente S (2012) Letter to the Editor. Chem Eng Process 51:34

    Google Scholar 

  88. Chen Q, Liang XG, Guo ZY (2013) Entransy theory for the optimization of heat transfer-A review and update. Int J Heat Mass Transf 63:65–81

    Google Scholar 

  89. Chen Q, Wang M, Pan N et al (2012) Reply to letter to the Editor. Chem Eng Process 56:35–36

    Google Scholar 

  90. Chen LG, Wei SH, Sun FR (2008) Constructal entransy dissipation minimization for ‘volume-point’ heat conduction. J Phys D Appl Phys 41:195506

    Google Scholar 

  91. Cheng XT, Xu XH, Liang XG (2011) Application of entransy to optimization design for parallel thermal network of thermal control system in spacecraft. Sci China Technol Sci 54:964–971

    Google Scholar 

  92. Wang WH, Cheng XT, Liang XG (2013) Entransy dissipation, entransy-dissipation-based thermal resistance and optimization of one-stream hybrid thermal network. Sci China Technol Sci 56:529–536

    Google Scholar 

  93. Cheng XT, Liang XG (2014) Application of entransy optimization to one-stream series-wound and parallel heat exchanger networks. Heat Transf Eng 35:985–995

    Google Scholar 

  94. Cheng XT, Liang XG (2013) Analyses of entropy generation and heat entransy loss in heat transfer and heat-work conversion. Int J Heat Mass Transf 64:903–909

    Google Scholar 

  95. Chen Q, Wang M, Pan N et al (2009) Optimization principles for convective heat transfer. Energy 34:1199–1206

    Google Scholar 

  96. Witte LC, Shamsundar N (1983) A thermodynamic efficiency concept for heat exchange devices. J Eng Power 105:199–203

    Google Scholar 

  97. Xu ZM, Yang SR (1996) A modified entropy generation number for heat exchangers. J Therm Sci 5:257–263

    Google Scholar 

  98. Hesselgreaves JE (2000) Rationalisation of second law analysis of heat exchangers. Int J Heat Mass Transf 43:4189–4204

    Google Scholar 

  99. Ogiso K (2003) Duality of heat exchanger performance in balanced counter-flow systems. ASME J Heat Transf 125:530–532

    Google Scholar 

  100. Cheng XT, Liang XG (2014) A comparison between the entropy generation in terms of thermal conductance and generalized thermal resistance in heat exchanger analyses. Int J Heat Mass Transf 76:263–267

    Google Scholar 

  101. Cheng XT, Liang XG (2013) Discussion on the applicability of entropy generation minimization to analyses and optimizations of thermodynamic processes. Energy Convers Manag 73:121–127

    Google Scholar 

  102. Salamon P, Hoffmann KH, Schubert S et al (2001) What conditions make minimum entropy production equivalent to maximum power production? J Non-Equilib Thermodyn 26:73–83

    Google Scholar 

  103. Cheng XT, Liang XG (2013) Applicability of minimum entropy generation method to optimizing thermodynamic cycles. Chin Phys B 22:010508

    Google Scholar 

  104. Guo ZY (2014) Comments on “The thermodynamic basis of entransy and entransy dissipation” [Energy 36 (2011) 4272–4277]. Energy 68:998–999

    Google Scholar 

  105. Cheng XT, Liang XG (2014) Discussion on the application of entransy theory to heat-work conversion processes. Acta Phys Sin 63:190501 (in Chinese)

    Google Scholar 

  106. Açıkkalp E (2014) Entransy analysis of irreversible Carnot-like heat engine and refrigeration cycles and the relationships among various thermodynamic parameters. Energy Convers Manag 80:535–542

    Google Scholar 

  107. Açıkkalp E (2014) Entransy analysis of irreversible heat pump using Newton and Dulong–Petit heat transfer laws and relations with its performance. Energy Convers Manag 86:792–800

    Google Scholar 

  108. Cheng XT, Liang XG (2014) Comments on “Entransy analysis of irreversible Carnot-like heat engine and refrigeration cycles and the relationships among various thermodynamic parameters” (Emin Açikkalp, Energy Convers. Manage. 80 (2014) 535–542) and “Entransy analysis of irreversible heat pump using Newton and Dulong-Petit heat transfer laws and relations with its performance” (Emin Açikkalp, Energy Convers. Manage. 86 (2014) 792–800). Energy Convers Manag 87:1052–1053

  109. Açıkkalp E (2014) Reply to comments on “Entransy analysis of irreversible Carnot-like heat engine and refrigeration cycles and the relationships among various thermodynamic parameters” (Emin Açikkalp, Energy Convers Manage 80 (2014) 535–542) and “Entransy analysis of irreversible heat pump using Newton and Dulong-Petit heat transfer laws and relations with its performance” (Emin Açikkalp, Energy Convers Manage 86 (2014) 792–800). Energy Convers Manag 87:1054–1055

  110. Grazzini G, Borchiellini R, Lucia U (2013) Entropy versus entransy. J Non-Equilib Thermodyn 38:259–271

    Google Scholar 

  111. Herwig H (2014) Do we really need “entransy”? A critical assessment of a new quantity in heat transfer analysis. J Heat Transf 136:045501

    Google Scholar 

  112. Awad MM (2014) Discussion: “entransy is now clear”. J Heat Transf 136:095502

    Google Scholar 

  113. Guo ZY (2014) Closure to “Discussion of ‘“Entransy,” and its lack of content in physics’” (2014, ASME J Heat Transfer, 136(5), p. 055501). J Heat Transf 136:056001

  114. Guo ZY, Chen Q, Liang XG (2014) Closure to “discussion of ‘do we really need “entransy”?’”. J Heat Transf 136:046001

    Google Scholar 

  115. Manjunath K, Kaushik SC (2014) Second law thermodynamic study of heat exchangers: a review. Renew Sustain Energy Rev 40:348–374

    Google Scholar 

  116. Chen Q, Guo ZY, Liang XG (2014) Closure to “discussion of ‘entransy is now clear’” (2014, ASME J Heat Transfer, 136(9), p. 095502). J Heat Transf 136:096001

  117. Kashani AHA, Maddahi A, Hajabdollahi H (2013) Thermal-economic optimization of an air-cooled heat exchanger unit. Appl Therm Eng 54:43–55

    Google Scholar 

  118. Cheng XT, Xu XH, Liang XG (2009) Homogenization of temperature field and temperature gradient field. Sci China Ser E Technol Sci 52:2937–2942

    Google Scholar 

  119. Wang WH, Cheng XT, Liang XG (2013) Analyses of the endoreversible Carnot cycle with entropy generation minimization and entransy theory. Chin Phys B 22:110506

    Google Scholar 

  120. Al-Sulaiman FA, Dincer I, Hamdullahpur F (2013) Thermoeconomic optimization of three trigeneration systems using organic Rankine cycles: part I—formulations. Energy Convers Manag 69:199–208

    Google Scholar 

  121. Curzon FL, Ahlborn B (1975) Efficiency of a Carnot engine at maximum power output. Am J Phys 43:22–24

    Google Scholar 

  122. Angulo-Brown F, Paez-Hernandez R (1993) Endoreversible thermal cycle with a nonlinear heat transfer law. J Appl Phys 74:2216–2219

    Google Scholar 

  123. Vos AD (1995) Endoreversible thermoeconomics. Energy Convers Manag 36:1–5

    Google Scholar 

  124. Wang WH, Cheng XT, Liang XG (2012) Entransy dissipation and irreversibility of some thermodynamic processes. Chin Sci Bull 57:4091–4099

    Google Scholar 

  125. Cheng XT, Liang XG (2013) The ability to do work indirectly for closed systems and its measurement. Sci China Technol Sci 43:943–947

    Google Scholar 

Download references

Acknowledgments

This work was supported by the National Natural Science Foundation of China (51376101).

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Xue-Tao Cheng.

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Cheng, XT., Liang, XG. Entransy: its physical basis, applications and limitations. Chin. Sci. Bull. 59, 5309–5323 (2014). https://doi.org/10.1007/s11434-014-0661-3

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11434-014-0661-3

Keywords