Regular compensation of equilibration processes with uphill ones requires a systematic work on the internal structure of the organism. In order to initiate uphill processes, regenerating nonequilibrium structures, gradients and potentials, living organisms must be able to work continuously against the thermodynamic equilibrium that otherwise ultimately would be reached given the actual instantaneous state of the organism on the basis of physical laws. This simplified chain of thoughts points towards the Bauer principle. The Bauer principle in its full form tells that "The living and only the living systems are never in equilibrium, and, on the debit of their free energy, they continuously invest work against the realization of the equilibrium which should occur within the given outer conditions on the basis of the physical and chemical laws." Bauer had shown that this is the first principle of biology, since all the fundamental phenomena of life can be derived from it (Bauer, 1935/1967, 51).
Let us formulate this compact definition in elementary statements. Requirement (a) tells that living systems are never in equilibrium. Requirement (b) tells that on the debit of their free energy content, they continuously invest work against the realization of the equilibrium which should occur within the given outer (initial and boundary) conditions on the basis of the physical and chemical laws. We can break requirement (b) into (b1) requiring continuous and self-initiated work investment AW in order (b2) to initiate a behavior differing from the one determined by the laws of physics and chemistry. In our understanding, (b1) and (b2) tells that the investment of work AW must be thermodynami-cally uphill. Moreover, (b2) tells that if the considered system has elementary constituents with coordinates xi, their spatial coordinates R have to differ in time from the one expected on the basis of physical and chemical laws, given the initial conditions. This means that the spatial trajectory of the constituent parts differ from the physical one by an amount AR(xi, t). It is not allowed to simplify the Bauer principle to its requirement (a), or misinterpret it as requiring only the "avoidance of thermodynamic equilibrium". As our detailed analysis clearly shows, only the simultaneous fulfillment of all the three requirements (a), (b1) and (b2) is equivalent with the Bauer principle.
It is usual to consider that in physically spontaneous processes entropy can only increase. Actually, when a piece of matter exists in a colder/hotter environment, its entropy S will decrease/increase in the equilibration. Moreover, the free energy is defined through the change of the chemical potentialyrelative to the standard state corresponding to Ty=298.16 Kandpy = 1 atm(Haynie, 2001, 81).
Therefore, the change of the entropy AS (and AG, the Gibbs free energy) of the system is not always a good indicator of thermodynamically downhill processes occurring within the considered system. Instead, thermodynamically downhill or equilibrating processes of physico-chemical systems can be characterized by the decrease of extropy n, the distance from equilibrium (Martinas and Grandpierre, 2007) of the system (An < 0). We define thermodynamically uphill processes here as processes in which the extropy of the system increases, An > 0. Extropy is measured relative to the environment; therefore it always decreases in equilibration or downhill processes.
Systems receiving positive extropy flow from their environment, like self-organizing physical systems, or like living organisms, can manifest structure formation. In terms of extropy, one can formulate the Bauer principle as requiring an investment of work AW in order to initiate uphill processes An > 0 compensating the equilibrating processes An < 0 occurring in the system.
Now let us consider how the Bauer principle applies to physical self-organizing systems. Self-organizing physical systems like Benard-convection cells in a fluid heated from below have constant energy supply (through incoming energy flow from below) and extropy supply (they receive higher quality energy at their input and release lower quality energy at their output) and so their distance from thermodynamic equilibrium can be constant. The permanent transformation of higher quality energy into lower quality energy can be described as an extropy flow through the system maintaining the structure and internal organization in the cell balancing the downhill process of radiated heat. For such systems, the change of extropy within the system can be practically zero, An ~ 0, without any investment of systematic work by the Benard cells themselves. Instead, their behavior is described by the laws of physics. This means that Benard cells do not fit the (b1) and (b2) requirements of Bauer principle.
We define a process as thermodynamically spontaneous if it occurs spontaneously, without any non-thermodynamic influence or intervention. Equilibrating processes occur by themselves, they are thermodynamically spontaneous. In comparison, we define a process as biologically spontaneous if it occurs spontaneously in the presence of biological couplings. Active transport regenerating a gradient is an uphill process; it cannot occur spontaneously in thermodynamics but can occur spontaneously in biology in the presence of suitable conditions and biological couplings. Now let us compare the range of physically spontaneous and biologically spontaneous processes. Although physical spontaneity is wide-ranged, including spontaneous emission, spontaneous absorption or spontaneous energy focusing at the wheel of a breaking car, biological spontaneity is much more wide-ranged, since it includes an astronomically rich realm of uphill processes which cannot occur spontaneously in thermodynamics. Therefore, systematic work investment also cannot occur spontaneously in thermodynamics. On the other hand, systematic work investment is a basic characteristic of living organisms required by the first principle of biology.
Complexity enters into the scene because systematically directed useful work is possible only by systems having a significant rate of algorithmic complexity. This is why machines require delicate planning and realization of a task-solving procedure having an algorithmic complexity. All machines serve some need or function. To obtain biologically useful, thermodynamically uphill work, living organisms must have extremely large algorithmic complexity. The first principle of biology holds that biologically useful work is exerted spontaneously in any part of the system in such a way as to promote the biologically optimal range, which corresponds to the characteristic distance of the organism from equilibrium.
Let us consider a simple example. A burning candle does not invest work on the debit of its free energy content. It does not have algorithmic complexity content in its structure. It does not fulfill requirements (b1) and (b2), therefore it cannot be regarded as living.
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