Physical Activity Level (PAL), Entropy Generation, Lifespan

Pubblicato: novembre 16, 2012 in general, health

Entropy Generation and Human Aging: Lifespan Entropy and
Effect of Physical Activity Level
Carlos Silva and Kalyan Annamalai *
Department of Mechanical Engineering, Texas A&M University, College Station, Texas 77843-3123,
USA; E-mails:;

Abstract: The first and second laws of thermodynamics were applied to biochemical
reactions typical of human metabolism. An open-system model was used for a human
body. Energy conservation, availability and entropy balances were performed to obtain the
entropy generated for the main food components. Quantitative results for entropy
generation were obtained as a function of age using the databases from the U.S. Food and
Nutrition Board (FNB) and Centers for Disease Control and Prevention (CDC), which
provide energy requirements and food intake composition as a function of age, weight and
stature. Numerical integration was performed through human lifespan for different levels
of physical activity. Results were presented and analyzed. Entropy generated over the
lifespan of average individuals (natural death) was found to be 11,404 kJ/ºK per kg of body
mass with a rate of generation three times higher on infants than on the elderly. The
entropy generated predicts a life span of 73.78 and 81.61 years for the average U.S. male
and female individuals respectively, which are values that closely match the average
lifespan from statistics (74.63 and 80.36 years). From the analysis of the effect of different
activity levels, it is shown that entropy generated increases with physical activity,
suggesting that exercise should be kept to a “healthy minimum” if entropy generation is to
be minimized.
Keywords: Biothermodynamics, Metabolism, Entropy, Entropy generation, Human
lifespan, Aging, Biological system


Properties of Nutrients

Snap 2012-11-14 at 13.03

PAL walking equivalences

Snap 2012-11-14 at 13.04


Entropy generation rate for the base case

Snap 2012-11-14 at 13.04

Cumulative Entropy generation for the base case

Snap 2012-11-14 at 13.05


Entropy generation base case data, 50th percentile population

Male Female

Av. Lifespan [5] 74.63 80.36

Entropy generated
(kJ/kg-K) 11 508 11 299

Change in lifespan vs. physical activity level (PAL)

Lifespan to limit
Case Male Female
S – Sedentary 85.05 95.75
LA – Low Active (base) 73.78 81.61
A – Active 63.78 69.53
VA – Very Active 53.20 57.68

Entropy Generation rate for different physical activity levels

Snap 2012-11-14 at 13.06


Cumulative Entropy Generation for different physical activity levels

Snap 2012-11-14 at 13.06



o The basic laws of thermodynamics were applied to biological systems, using a combination of laws
of thermodynamics and available information from biochemistry literature and updated CDC
databases. Entropy generated was determined for metabolism of the typical components of the
human diet, and total entropy generation was estimated through numerical integration for the
average population.

o Data on average lifespan was used to obtain lifetime limit entropy, which was found equal to
11,404 kJ/kg-K. This value of entropy predicts life span within 1.5% of the life span from literature
(predicted: 73.78 and 81.61 years; Literature: 74.63 and 80.36 years; males and females

o Entropy generation rate was found to be 3 times higher on babies than on elderly, and in general,
lifetime entropy curves showed similar trends and values to those of the previous work of Hershey
and Wang [24, 25], though the values obtained in this work are approximately 5-10% higher.

o The higher the specific metabolic rate (kW/kg), the higher the specific entropy generation rate
(kW/kg), and the faster we approach the specific entropy generation limit over a lifetime (kJ/kg K).

o The entropy generation rate depends upon the type of ration fed to BS.

o When a non-zero gravity environment is approximated as a change from low active to sedentary
PAL, it is possible to predict changes on the lifespan of astronauts based on the exposition time to
the weightless condition. It was found that a male astronaut will extend his life span 1 year for
every 9.5 years he spent in space. For a female astronaut, this time was estimated as 7.5 years.

o The present approach presumes that the ATP acts as work currency, generating no entropy.

o While the present analysis for entropy generation is conducted considering the human as a whole
system, the analysis can be extended to determine the entropy generation for each organ of the
system (heart, kidney, liver etc) and to determine which degenerates rapidly as long as metabolic
rates and metabolic efficiencies of the organ are known.


Entropy 2008, 10, 100-123; DOI: 10.3390/entropy-e10020100



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