Mathematical absurdities in the California net energy system

Carl A. Old, Ian J. Lean, Heidi A Rossow

Research output: Contribution to journalArticlepeer-review

1 Scopus citations


Net energy systems, such as the California Net Energy System (CNES), are useful for prediction of input:output relationships not because of fidelity to the laws of thermodynamics, but because they were designed to predict well. Unless model descriptions of input:output relationships are consistent with the laws of thermodynamics, conclusions regarding those relationships may be incorrect. Heat energy (HE) + recovered energy (RE) = ME intake (MEI) is basic to descriptions of energy utilization found in the CNES and is consistent with the laws of thermodynamics; it may be the only relationship described in the CNES consistent with the first law of thermodynamics. In the CNES, efficiencies of ME utilization for maintenance (km) and gain (kg) were estimated using ordinary least squares (OLS) equations. Efficiencies thus estimated using static linear models are often inconsistent with the biochemistry of processes underlying maintenance and gain. Reactions in support of oxidative mitochondrial metabolism are thermodynamically favorable and irreversible; these reactions yield ATP, or other high-energy phosphate bonds, used for what is generally termed maintenance. Synthesis of biomass (gain) is less thermodynamically favorable; reactions do not proceed unless coupled with hydrolysis of high-energy phosphate bonds and lie closer to equilibrium than those in support of oxidative mitochondrial metabolism. The opposite is described in the CNES (km > kg) due to failure of partitioning of HE; insufficient HE is accounted for in maintenance. Efficiencies of ME utilization (km and kg) as described in the CNES are variable. Further neither km nor kg are uniformly monotonic f(ME, Mcal/kg); for ME (Mcal/kg) <0.512 or >4.26, km are inconsistent with thermodynamically allowed values for efficiencies (>1.0); kg are a monotonically positive f(ME) concentration (Mcal/kg) for ME <3.27 Mcal/kg. For ME <1.42 Mcal/kg, kg are not in the range of thermodynamically allowed values for efficiencies (0 to 1.0). Variable efficiencies of ME utilization require that the first law may not be observed in all cases. The CNES is an excellent empirical tool for prediction of input:output relationship, but many CNES parameter estimates evaluated in this study lack consistency with biology and the laws of thermodynamics.

Original languageEnglish (US)
Article numbertxz020
Pages (from-to)1018-1028
Number of pages11
JournalTranslational Animal Science
Issue number3
StatePublished - Jun 25 2019


  • beef cattle
  • efficiency
  • maintenance

ASJC Scopus subject areas

  • Animal Science and Zoology
  • veterinary(all)


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