The Second law of
Thermodynamics
Seytkasymova Nurbakyt
The second principle of thermodynamics
 The second principle of thermodynamics states that an isolated system moves
spontaneously towards a maximum in its entropy. When this state is achieved,
then the system is in thermodynamic equilibrium. In the same way, the decrease
of the free energy down to a minimum can be considered as the way towards the
equilibrium in the sense of the second principle.
 Any movement as a result of energy transformation leads to an increase in the
entropy of the system or its environment. The term entropy production (σ =
dS/dt) has been introduced to characterize this process. The entropy production
is always positive, but can approach zero. The condition: σ = 0 would mean an
idealized reversible process. Thermodynamically, a process is defined as being
reversible if it can be repeated an arbitrary number of times without requiring
the supply of additional energy.
Some Fundamental Concepts of Thermodynamics
 To prevent misunderstanding, the different
meanings of the term “reversible” in physics,
chemistry, and biology must be pointed out. In
physics, the term “reversible” is used according to
the thermodynamic definition, i.e., connected with
the above-mentioned condition: σ = 0. When a
chemist speaks about a “reversible reaction,” or a
“reversible electrode,” he only means processes
that in principle could run in both directions,
independently of the required energy. Finally, the
biologist states that a change in a biological system
is “reversible” when it is able to reverse an induced
change so that no irreparable damage is caused (for
example: reversible inhibition of metabolic
processes).
 Let us consider the total entropy balance of a system. In closed
systems, as a result of energy transformations, only an entropy
increase is possible up to the point where the thermodynamic
equilibrium is established without any further entropyproducing
processes. In open systems, however, which are able to exchange
not only energy but additionally matter, the entropy may change
in both directions. An entropy decrease can occur if substances
with low entropy content are incorporated, in exchange for
entropy-rich substances that are being extruded. To characterize
this process, an entropy flux (JS) is formulated which penetrates
the whole system. Hence, the total entropy balance of the system
can be written as follows:
Energetics and Dynamics of Biological Systems
Let us illustrate this statement with
an example:
Using radionuclides it is
possible to demonstrate that human erythrocytes exchange chloride as well aspotassium ions
with their environment. With this method, it is possible to measure
directly the corresponding exchange rates. This kinetic method of analysis may give
the impression that both ions, Cl, as well as +
K, are in a steady state because in
both cases the unidirectional fluxes, outside ! in and inside ! out, are equal.
This, however, is an incorrect conclusion. The chloride ions in fact are distributed
passively between the external medium and the cytoplasm, according to their
thermodynamic equilibrium.
Some Fundamental Concepts of Thermodynamics
An important property of all stationary states is their kind of stability. Let us
illustrate this by a mechanical example of a sphere on a surface (Fig. 3.5). The
requirement for a stationary state, in this case this simply means an equilibrium, is
the sphere coming to rest on any small, but horizontal part of the surface. In the case
of an indifferent state, the surface is horizontal in general. In this case the energy of
the sphere will not be changed by alteration of its position. In the case of a stable
114 3 Energetics and Dynamics of Biological Systems
state, every change of the position leads to an increase of the energy of the sphere,
and generates a force driving the sphere back to its original state. In contrast an
unstable state is characterized by a situation where even small changes of the
position release forces that cause the system to be deflected even more. Additionally sometimes so-called metastable
states are considered. As metastable, a stable
state can be considered which is delimitated from another one by a small barrier
which can easily be overcome
Figure 3.6 indicates all possible kinds of stationary states. First of all the
presence, or the absence of entropy production indicates whether the given stationary state is a thermodynamic
equilibrium (s ¼ 0), or whether it is a steady state
(s > 0).
In the case of thermodynamic equilibrium one must distinguish between
global and local equilibria. In the case of a global equilibrium, the function of free
energy indicates only one minimum. This means that no alteration, however strong
it may be, can bring the system into another equilibrium state. An example is the
equilibrium distribution of an ion between the cell and its environment. In contrast,
in the case of the local equilibrium, the energetic function indicates two or more
minima which are separated by more or less high energy barriers. As an example,
isotherms of biochemical reactions can be considered, as illustrated in Fig. 2.5. The
stability of such local equilibria is determined by the energy barrier between them.
If this barrier is so low that thermal fluctuations can lead to quick transitions, the
state is called metastable. This for example is the typical situation for enzymesubstrate
complexes. For the schemes in Fig. 3.6 it must be considered that in reality
G is not simply a function of a single reaction coordinate (x), but rather a hyperplane in ndimensional space
Some authors discuss this metabolic rate in context with
this Prigogine principle of minimal entropy production.
Figure 3.7 shows for example a mean scheme of the
characteristic situation in mice. While the total heat
production (Q_) increases in accordance with their age and
mass (m), the specific heat production, that is the heat
production relative to the body weight, i.e., the dissipation
function (F), reaches a maximum and then decreases. It
seems therefore that an animal in the state of Fig. 3.6
Possible types of stationary states and conditions of their
stability 116 3 Energetics and Dynamics of Biological
Systems development increases entropy production,
whereas an adult organism tends to arrive at a minimum.
Disturbances in life lead to various deflections from this
curve. If an organism for example is injured, if it is stressed
by some environmental conditions, or in the case of tumor
growth, the corresponding disturbances of the metabolism
lead to a temporary increase in the slope of the curve.
Figure 3.8 shows some characteristic
times on a logarithmic scale that will
serve to extend this list of examples.