Entropy and Life

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Many regard 1944 as the year in which biophysics was founded, with the publication of Erwin Schrodinger's What Is Life?. Winner of the Nobel Prize for Physics and father of quantum mechanics, in this publication he expresses his thoughts on biological problems. He introduces the concept of negentropy, underlining that it is a negative variant of entropy from an initial value (the birth of the individual, the origin of life, the beginning of biological evolution) and not of absolute negative entropy, since the third law of thermodynamics does not conceive of an entropy value less than zero. ''How would we express in terms of the statistical theory the marvellous faculty of a living organism, by which it delays the decay into thermodynamical equilibrium (death)? We said before that it feeds on negentropy, attracting, as it were, a stream of negative entropy upon itself, to compensate the entropy increase it produces by living and thus to maintain itself on a stationary and fairly low entropy level.''

According to Boltzmann, the struggle for life is not a struggle for basic elements or energy but for the entropy (negative) available in the transfer from the hot Sun to the cold Earth. Utilizing this transfer to a maximum, plants force solar energy to perform chemical reactions before it reaches the thermal level of the Earth's surface. The paths of these reactions are unexplored and still impossible in our laboratories.

Thermodynamics reigns throughout science from mechanics to nature but the natural biological laws of evolution seem to contradict it. Biological systems apparently violate the second law, they show extremely ordered structures and evolve in a direction of increasing order or less entropy. The contradiction is really only one of appearance. The entropy balance must be total and must include both biological organisms and the environment with which the organism continually exchanges energy and matter. Thus biological organisms develop and live by virtue of the increased entropy which their metabolism provokes in the surrounding environment. The total change in entropy is positive: the entropy of the universe increases and the second law is not violated.

If bacteria are allowed to reproduce in glucose solution, part of the sugar can be seen to cause a decrease in entropy, being transformed into cell components. The rest is transformed into carbon dioxide and water, leading to an overall increase in entropy.

It is necessary to distinguish between isolated systems (which cannot exchange energy or matter with the outside world), closed systems (which can exchange energy but not matter, e.g., our planet), and open systems (which can exchange both energy and matter). Cities and biological organisms are examples of open systems. For such systems we must sum the negative entropy produced inside the system with the positive entropy created in the environment. We then see that if 'sometimes disorder degenerates into order' this is only a facade, the appearance of order at the price of even greater disorder in the surrounding environment. Living systems therefore need a continuous flux of negative entropy from the universe, to which they return an even larger amount of positive entropy. Ilya Prigogine called these open systems 'dissi-pative structures'. The flow of energy causes fluctuations in the dissipative structure which reorganizes tending to a higher level of complexity. As such it requires an even higher energy input and is even more vulnerable to fluctuations. It reorganizes again in continuous biological evolution toward complexity and higher energy needs.

The entropy concept has rarely been studied in biology, although, from a thermodynamical viewpoint, entropy is the key concept in the second law and the only concept in the physical science having directionality with time.

Biological phenomena have directionality with time in their trends and, for this reason application of the entropy concept to biology would lead to a deeper understanding of living systems. An entropy viewpoint is actually required to study these systems.

However, there are conceptual and methodological difficulties in the measurement and estimation of the entropy content of living systems. In contrast, entropy-related quantities, that is, entropy production and entropy fluxes, can be estimated by use of some physical methods from observed energetic data of biological objects.

In general, for an open chemically reactive system of n constituents that exchanges energy or matter with the environment through the surface X, it is possible to write entropy as a function of the local entropy density sv:

where sv = sv(pi (r, t), ..., p„(r, t)), being pi ... p„ the composition variables, r the spatial variable, and t time. Deriving the entropy density with respect to time and using the local mass balance (thermodynamics' first principle) it is possible to demonstrate the relation

where Js is the matrix of the external entropic fluxes through u and u is the internal entropy production, which in general can be written as

where Jk are the rates of the various irreversible processes involved (chemical reactions, heat flow, diffusion, etc.) and Xk the corresponding generalized forces (affinities, gradients of temperature, of chemical potentials, etc.).

Integrating the entropy density over the volume and applying the Gauss divergence theorem we obtain

Now we have a suitable formulation and a powerful tool to understand how the entropy variation in open systems is the sum of two terms: external entropy fluxes and internal entropy production.

From a thermodynamical viewpoint, any ecosystem is an open system far from thermodynamic equilibrium, in which entropy production is balanced by the outflow of entropy to the environment. Eugene Odum in 1989 has argued that an integral part of the ecosystem concept is a model of an open, thermodynamic nonequilibrium system, with the emphasis on the external environment. The climax of the ecosystem corresponds to a dynamic equilibrium (steady state), when the entropy production inside a system is balanced by the entropy flow from the system to its environment.

In the theory of open systems and dissipative structures by Ilya Prigogine, as we have seen above, the total variation of entropy is presented in the form of two items:

where d^z) is the entropy production (heat, disorder) caused by irreversible processes within the system and deS(z) corresponds to the entropy of exchange processes between the system and its environment; it is the transfer of entropy across the boundaries of the system.

In this formulation, the distinction between irreversible and reversible processes is essential. Only irreversible processes produce entropy. The second principle therefore states that irreversible processes lead to a sort of unidirectional time. For isolated systems deS = 0 and the previous equations becomes the classical second law. Open systems could conceivably evolve to steady states with deS = - diS, dS = 0 [9]

This is a nonequilibrium steady state that should not be confused with thermodynamic equilibrium, and in which order may be created from disorder. Order created in this way no longer violates the laws of thermodynamics; equilibrium is no longer the only attractor of the system, but the world becomes more complex and thermodynamics can embrace new worlds characterized by highly organized as well as chaotic structures.

Prigogine illustrates this entropic behavior using the concept of entropy production (see Figure 1).

The simplest example of a self-organizing system is the Benard instability, in which a viscous fluid is heated

Evolution toward equilibrium

Equilibrium

Evolution toward steady state

Steady state

deS < 0

deS = 0

deS < 0

deS diS dt dt deS < 0

Se

diS i > 0 dt

diS i > 0 dt

- const * 0 dt

diS > 0 i

diS = 0

diS > 0

diS > 0

Si

dS = diS + deS < 0

S

dS = diS + deS > 0

dS = 0

V

dS = 0

f

S = max

S = min

Figure 1 Entropy variations in four different cases.

between two planes (or plates, to eliminate surface effects) in a gravitational field. There is a critical value of the Rayleigh number at which fluctuations in the density of the fluid overcome the viscosity faster than they are dissipated. These fluctuations are amplified and give rise to a macroscopic coherent circular current, a spatially ordered dissipative structure.

Morowitz applied the Prigogine considerations about open systems to the biosphere. He realized that the second law of thermodynamics applies to systems close to equilibrium, whereas the ecosystems and the surface of the Earth, the matrix of biological evolution, belongs to a different class of physical systems. Systems in equilibrium must be either adiabatic (isolated) or isothermal. However, the biosphere is quite another type of physical system, in contact with various sources and sinks, and with matter and energy flowing through it from the sources to the sinks.

Let us consider the following flow diagram:

Energy sources ! Intermediate system (biosphere) ! Sinks

Let us now consider the system divided in two parts:

2. intermediate system (i)

According to the second law of thermodynamics dSs + dSi > 0 [10]

where Ss is the entropy of source + sink and Si is the entropy of the intermediate system. The flow of energy from the source to the sink will always involve an increase in entropy:

whereas the only restriction placed by the second law of thermodynamics on dSi is that

so that the entropy of the intermediate system (in our case the biosphere) can decrease if there is an energy flow. A flow of energy provides the intermediate system (the Earth's surface) with quantities of energy for the creation of states far from equilibrium, that is, far from thermal death. The farther the nonequilibrium system is from equilibrium, the more ordered it is. The ordered state of a biological system would decay, if left to itself, toward the most disorderly state possible. This is why work must continuously be done to order the system. As we have seen, this requires a hot source and a cold sink, the Sun and outer space.

The surface of the Earth (intermediate system) receives a flow of energy from the Sun source at 5800 K

(temperature of the surface of the Sun; the core of the Sun is millions of degrees hotter) and returns it to the sink of outer space at 3 K. In this vast temperature range lies the secret of life and the possibility of work against entropic equilibrium, moving the living system away from equilibrium, toward ordered, negentropic, alive states. The living system is maintained in a 'steady state' as far as possible from equilibrium by the flow of energy E. Solar energy is distributed over its spectrum as follows (molecular changes induced are within brackets): 0.02% far ultraviolet (ionization); 7.27% ultraviolet (electron transitions and ionization); 51.73% visible (electron transitions); 38.90% near infrared (electron and vibrational transitions); 2.1% infrared (rotational and vibrational transitions). A small fraction is fixed chemically by photosynthesizing organisms. This energy is the prime mover of biological transformations, including the main nutritional cycles. Global ecological processes are characterized by chemical cycles, such as the carbon and nitrogen cycles. The solar energy reaching the Earth is about 5.6 x 1024J but, E, normally accepted, after correction for albedo, is 3.93 x 1024J.

The decrease in entropy (negentropy) in the biosphere depends on its capacity to capture energy from the Sun and to retransmit it to space in the form of infrared radiation (positive entropy). If retransmission is prevented, in other words, if the planet were shrouded in an adiabatic membrane (greenhouse effect), all living processes would cease very quickly and the system would decay toward the equilibrium state, that is, toward thermal death. A sink is just as necessary for life as a source.

Morowitz continues that all biological processes depend on the absorption ofsolar photons and the transfer of heat to the celestial sinks. The Sun would not be a negentropy source if there were not a sink for the flow of thermal energy. The surface of the Earth is at a constant total energy, reemitting as much energy as it absorbs. The subtle difference is that it is not energy per se that makes life continue but the flow of energy through the system. The global ecological system or biosphere can be defined as the part of the Earth's surface that is ordered by the flow of energy by means of the process of photosynthesis.

The physical chemistry mechanism was elegantly described by Nobel Prize winner Albert Szent-Gyorgy as the common knowledge that the ultimate source of all our energy and negative entropy is the Sun. When a photon interacts with a particle of matter on our globe, it raises an electron or a pair of electrons to a higher energy level. This excited state usually has a brief life and the electron falls back to its basic level in giving up its energy in one way or another. Life has learned to capture the electron in the excited state, to uncouple it from its partner, and to let it decay to its fundamental level through the biological machinery, using the extra energy for vital processes.

All biological processes, therefore, take place because they are fuelled by solar energy. Morowitz notes that it is this tension between photosynthetic construction and thermal degradation that sustains the global operation of the biosphere and the great ecological cycles.

This entropic behavior marks the difference between living systems and dead things.

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