Entropy

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# Abstract

Perpetual confusion exists even today regarding the application of laws of thermodynamics to living systems mainly due to misinterpretation of entropy, its nature, ignorance of statistical thermodynamics and Gibbs ensembles.

### Introduction

Perpetual confusion exists even today regarding the application of laws of thermodynamics to living systems mainly due to misinterpretation of entropy, its nature and ignorance about the importance of statistical thermodynamics.

### The first law of thermodynamics

The first law of thermodynamics is about conservation of energy which may be stated as “energy is neither created nor destroyed”. However the energy may be transformed from one form to the other.

### Entropy, second and third laws of thermodynamics

Rudolf Clausius [Rudolf Julius Emanuel Clausis] a German physicist and mathematician coined the word entropy1, 2 in the year 1865 in his paper “on the mechanical theory of heat” which literally means transformation to describe the tendency of energy to transform to less and less valuable forms – the dissipation of energy. Entropy is the extensive property of the system. Entropy in other words is unused or wasted energy that is dissipated by the system into its surrounding.

The change in the entropy is related to the change in the amount of heat absorbed in the following manner.

[a] spontaneous process        :    dS > δQ/T        [1]
[b] equilibrium process           :    dS = δQ/T        [2]
[c] non spontaneous process  :    dS < δQ/T        [3]

The quantity δQ/T, the ratio of heat absorbed to the temperature is called reduced heat. Spontaneous processes are those that can proceed on their own for example transfer of heat from a hotter part of a system to a colder part, mixing of gases and equilibration of the pressure of a gas. For a non spontaneous process to occur expenditure of external work is required. For systems where no heat transfer is involved that is δQ = 0, the following relations are valid.

[d] spontaneous process        :        dS > 0        [4]
[e] equilibrium process           :        dS = 0        [5]
[f] non spontaneous process   :        dS < 0        [6]

At this juncture we need to know about thermodynamic systems. The following definitions are being reproduced3, 4 from Wikipedia.

### Boundary and surrounding

A system boundary is a real or imaginary volumetric demarcation region drawn around a thermodynamic system across which quantities such as heat, mass and work can flow3, 4 that is a boundary is what separates the system and its surroundings. Thus surrounding is what lies out side the system or surrounding is the environment in which the system operates. An isolated system is one that does not exchange heat, mass or work with its surroundings. A closed system does not exchange mass with its surroundings but exchanges heat and work. An open system does exchange heat, mass and work with the surroundings.

The second law of thermodynamics is stated as, “The entropy of an isolated system either increases or remains constant” which is expressed as follows:-
dS ≥ 0            [7]
And dS > 0, expresses the criterion of spontaneity for a process occurring in an isolated system. For processes involving heat exchange, the following expression is used.
dS ≥ δQ/T        [8]

The above expressions lead us to understand2 that an increase in entropy is either equal to the reduced heat for equilibrium (reversible) processes or greater than the reduced heat for non equilibrium (irreversible) processes. Thus the entropy is a property associated, on the one hand, with heat exchange and on the other hand with irreversibility. This dual nature of entropy is better understood not from the stand point of classical propositions of Clausius but from the stand point of molecular statistics in terms of order-disorder of the motion or state of its constituent particles. According to Planck (the third law of thermodynamics) the entropy of a crystal with perfect structure near absolute zero temperature tends to zero. An increase in the temperature of the crystal causes vibration of particles at the lattice points with different energies leading to increased disorder that is increased entropy. An increase in entropy that is disorder is possible2 without involving heat transfer in non equilibrium systems described by equation [4].

### Closing remarks

While applying thermodynamics to living systems the stand point of molecular statistics and the relation of entropy with order-disorder must always be kept in mind. Thermodynamic description of living systems is analogous to Gibbs grand canonical ensembles as discussed 5 earlier.

It follows from the classical version of second law that energy can’t be transformed into work by cent percent efficiency which also means that it is impossible to construct a machine that runs on its own consuming the energy generated by itself without drawing energy from external source. In other words it is impossible to construct a perpetual motion machine. The self drive of living systems is not same as perpetual motion machine as living systems generate the energy required for self drive from the food they consume from the external source. Interpreting self drive of living systems/ organism same as perpetual motion machine is erroneous.Genopsych is an extensive like emergent property but can not be reduced to the elements of the system and it is genopsych that distinguishes a living system from a physical system. Finally the functioning of genome is non spontaneous and so is the self drive of living systems/organism.

### References

1. Yeremin, E.N., Fundamentals of Chemical Thermodynamics, MIR Publishers, 1983, Moscow.
2. Perrot, Pierre A to Z of Thermodynamics. Oxford University Press, 1998. Cf(3).
3. Sekhar, DMR. Living Systems: Systems Biology [Internet]. Version 17. Knol. 2011 Mar 12. Available from: http://knol.google.com/k/dmr-sekhar/living-systems/3ecxygf1lxcn2/84.