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A simple and general theory to describe basic irreversible thermodynamic aspects of aging in all dissipative living is presented. Any dissipative system during its operation continuously loses efficiency by the production of structural or functional defects because of the second law of thermodynamics. This continuous loss of efficiency occurs on all the dissipative systems through the realization of specific functional cycles, leading to a maximum action principle of any system involving the Planck’s constant during their total dissipative operation. We applied our theory to the calculation of men and women lifespans from basal metabolic rate per unit weight and to the calculation of a new aging parameter per cycle of some human organs or physiological functions. All microscopic theory of the aging of living beings should be consistent with the second law of the thermodynamics. In other words, the operation of the biological self-organized structures only implies a delay in which the dissipative biological systems outside of equilibrium approach inexorably to the thermodynamic equilibrium obeying the second law of the thermodynamics.

From Schrödinger’s classic work published in 1944 [

The next step of the theoretical conception of living systems or non-living dissipative systems in a thermodynamical scheme was due to the Prigogine work in 1945, when the theorem of minimum entropy production applicable to non-equilibrium stationary states is published [

Additionally, to the previous information, it is an almost universal experimental fact that stationary states corresponding to dissipative structures do not last forever, despite being stable against fluctuations. Gradually, stationary states start to monotonically decline and eventually stop working to reach the thermodynamic equilibrium. For non-living dissipative systems, these processes could be defined as a process of intrinsic progressive loss of functionality, which conducts to ceasing of working properly, and eventually to failure [

Given the generality of the finite duration of stationary states in dissipative structures within irreversible thermodynamic processes, the following steps in a thermodynamical scheme, it is obligated. Let us try to use the second law of thermodynamics to describe the following facts. Section 2 contains a thermodynamical background necessary for our model. In Section 3, we present some empirical thermodynamical observations of living systems and present our very general theoretical formalism of an average dissipation rate theory taking into account the cyclic nature of living beings. In Section 4, we analyze in our formalism data comparing lifespans of human beings (females and males) and different human organs and physiological functions. Section 5 is devoted to conclusions.

First, let us make a brief synthesis of relevant general thermodynamical results.

The first law reads,

where the internal energy of the system is

with

Also we know [

tion of generalized fluxes

From this equation, it is possible to define the Raleigh’s dissipation function [

This represents the heat generation inside a system, and could be experimentally measured. For biological dissipative structures far from thermodynamic equilibrium, it is convenient to write Equation (4) per unit volume or per unit weight;

Prigogine [

where

forces. This result is valid provided the system is subject to time-independent boundary conditions, and it is the extension of the minimum entropy-production property to the non-linear domain of irreversible processes.

However, in contrast to inequality for linear irreversible thermodynamics

does not imply the stability of the steady-state, primarily because in the general case

It has been experimentally observed long time ago that during the time development of living systems, the dissipative Raleigh function per unit volume

The general schematic behavior of self-organized living dissipative structures is shown in

In our formalism, the initial time is the instant when the “egg” is formed, which depends on the type of living being. For instance, in a mammal, we consider that time starts with the fetus development, and for the birds, the

process depends on the heat received by the egg in the incubation process.

It is widely observed that most living dissipative systems perform functional cycles. For example in mammals breathing, heartbeat, digestive processes, etc. are cyclic processes. Of these, the most important functional cycle is the relative to the rate of arrival of nutrients and oxygen to each and every one of the cells that make up every living system. The heartbeats promote, throughout the body, a distribution of free energy per unit time which allows meeting the needs of the dissipative system. Clearly, for each process that occurs within the system, the length of each cycle varies with the age of each living being and that may depend on the specific activities carried out at all times. As a first approximation, the case of the cyclic dissipative systems will be analyzed, under the assumption that a large population of them can be represented by average values through their working life. Based on the second law of thermodynamics, is considered here that any living being gradually wears down and eventually stops working as it previously did (in a similar way that occurs for an internal combustion engine, which also operates through cycles).

During their operation dissipative systems perform internal processes of a cyclic nature that could be repeated hundreds, thousands or thousands of millions of times, etc. The dissipative structures go through a maximum number of cycles,

If we consider the whole process to take place at a constant temperature

In mathematical language

where

where

Thus, the total operation time of the dissipative system is given by

Which shows in a direct way that a dissipative system has a maximum of continuous time operation inversely proportional to the specific dissipative Raleigh’s function of the system, and directly proportional to their

It is clear that many dissipative structures realize functional cycles, which repeat over and over during its whole period of operation, before fail. Assuming, for simplicity, that the cycles are identical, then, from Equation (9):

Here

living machine performs one of the

In the sake of mathematical simplicity, constant or average duration of the functional cycles through life will be assumed, even though we know that during adulthood metabolism decreases in time, which causes that the time duration of cycles also diminish.

The existence of an upper limit to the number of the operation cycles implies also the existence of accumulative damage and aging processes. This damage and aging processes cause the continuous decreasing on the power that the dissipative can handle through time and from empirical observation is clear that the aging rate is different and characteristic for each type of system.

For auto-organized systems, there are many phenomenological observations, which show that the macroscopic symptoms of aging begin to appear after the auto-organized dissipative structure attains adulthood [

Taking into account such empirical information from macroscopic signs of aging it is possible to make an approximation about the derivative in time

where

Here

which clearly states that every dissipative structure necessarily suffers accumulative damage during its operation. We can say that the dissipative system has some functional memory, in the sense that cannot be rejuvenated. That is,

Neglecting the contribution of the collapse stage 4 (assuming that this last stage is extremely short as compared with the stage 3), also from Equation (14) it is easy to define a new physical macroscopically variable related to the steady-state of entropy production; the fractional remaining functionality:

Therefore,

From this equation, it is clear that when the dissipative system collapses,

By using Equation (17) into Equation (14)

which describes the time evolution of

which could be expressed as a function of the total cycle number at failure condition

Here

This equation shows, as expected, that fractional remaining functionality has high values, when the functional damage is low. For animals, these equations allow to see that at the time

dynamical limitations imposed by the functional damage

Here, by using our formalism, it is possible to obtain an equation for the maximum entropy changes in a dissipative system as multiples of the Boltzmann’s constant. For this purpose, let us employ another physical meaning

of Equation (9) if we use Equation (5), together with

i-dissipative system, it is possible to obtain the following equation:

where

of the i-system. Therefore, Equation (22) can be written as

where

Therefore, the total entropy generated during the continuous dissipative operation of the dissipative system,

Notice that physically and mathematically Equation (23) resembles the uncertainty principle due to Heisenberg;

where

By using Equation (25), into Equation (24) it is possible to obtain

where

In the following paragraphs, a comparison between the theoretical results here obtained with experimental data, and other theoretical considerations will be made.

First, we will give a quantitative thermodynamic explanation to experimental facts that on average (for all current country populations) women live several years more than men. Later, we will discuss some thermodynamic implications of aging of humans and their internal organs. On one hand, from ^{2} and 1.6 m^{2} respectively. Also from reference [

On the other hand, taking into account the female and male life expectancy of all the members of the European Union (EU) [

expectancy for the EU,

Therefore, the percentage difference between the theoretical and the experimental data is 2.5%, which is an excellent result.

There are two reasons for employing EU data; their data availability and very few premature deaths of that relatively rich, healthy and homogeneous population as compared to other regions of the world population. Premature deaths are due to crimes, war, disease, and malnutrition. For instance, in Sub-Saharan Africa, one of the worse health problems (if not the worst) is underweight infancy.

Relative to the thermodynamic implications of aging of humans and their internal organs, in

From data of Cutler et al. [

The data on

Organ or Human Function | Values of |
---|---|

Nerve | |

Basal Metabolic Rate | |

Filtration Rate of Kidney | |

Cardiac Output | |

Vital Lung Capacity | |

Maximum Breathing Capacity |

We identified general four chronological stages of self-organized living dissipative structures of the specific (per unit volume) production rate of entropy: 1) an initial more or less exponential transient stage, 2) stationary or steady-state stage, (adulthood), with slow aging, 3) aging in the mature stage” with an approximate linear decrease of

Based on the proposal of an average dissipation rate model for non-linear irreversible thermodynamics for dissipative structures, which goes through functional cycles, we conclude that the systems necessarily generate a maximum quantity of entropy (characteristic of each type) and, therefore, last a maximum quantity of time

The second law of thermodynamics has been used to explain the finite time duration of stationary states and simultaneously, both the processes of intrinsic progressive loss of functionality for non-living dissipative systems, and the processes of intrinsic progressive loss of organic function in the living dissipative systems. Some of the theoretical results (as Equation (10)) show in a direct way that all kinds of dissipative system have a maximum of continuous time operation inversely proportional to the specific dissipative Raleigh’s function of the system, and directly proportional to their

We hope that future developments of simple concepts developed here, such as fractional remaining functionality (Equation (16)), could to make a contribution to develop programs for preventive health care. Different values for corresponds to distinct aging rates on a given subsystem of human bodies. Then for a given organ (fundamental or not) it is possible to collect data of a human population and select the people with lower values for

Figures of the type of

Analogous to the quantum Heinsenberg’s principle, we presented an empirical principle for maximum action of any dissipative system involving the Planck’s constant.

We made use of average values of the basal metabolic rate per unit weight of European man and women to conclude that, on average, the human female last longer than the human males, with only a 2.5% of relative error. Also, we calculated the aging parameter measuring the functional decay of the dissipative system in each cycle from specific production of entropy of some human organs or physiological functions.

We assumed constant duration of the cycles in adulthood, even though we know that during adulthood, metabolism decreases in time. Then it will be desirable to refine our formalism to include different values of the average and the variance of the duration of the cycles in different stages of the living structures.

The substitution of organs as a way to increase the span of human life, we would have as limit the time implied by the aging rhythm of the original brain. In the same way that the inclusion of new pieces in an old car does not increase to infinite the lifespan of the car, since during the replacement process, a stage will be attained were the car rejuvenated no longer corresponds with the original car.

All microscopic theory of the aging of living beings should be consistent with the second law of the thermodynamics. In other words, the operation of the biological self-organized structures, is not more than an efficient mechanism of degradation of the free energy that we receive from the sun, and it only implies a delay in which the dissipative biological systems outside of equilibrium approach inexorably to the thermodynamic equilibrium obeying the second law of the thermodynamics.

JAMA specially wants to thanks to Prof. M. López de Haro for many years of deep discussions and arguments and by his contribution to final shaping of the ideas here developed.