Vol.2, No.1, 49-52 (2011) Journal of Biophysical Chemistry
Copyright © 2011 SciRes. Openly accessible at http://www.scirp.org/ journal/JBPC/
The asymmetry of time and the cellular world.
Is immortality possible?
Roberto O. Aquilano1,2
1Instituto de Física Rosario (CONICET-UNR), Rosario, Argentina; aquilano@ifir-conicet.gov.ar
2Facultad de Ciencias Exactas, Ingeniería y Agrimensura (UNR), Rosario, Argentina
Received 21 August 2010; revised 15 October 2010; accepted 10 November 2010.
I analyze the flow of time in this article, both in
gross and in microscopic processes, with a well
defined arrow of time, but as the amount of en-
ergy involved in the microscopic processes is
so small, it is more difficult to argue that the
entropy increases, and therefore the direction of
time becomes confusing and undefined at the
molecular level. Therefore, is cell immortality
Keywords: Entropy; Time; Cell
The concept of time is intuitive and easily distin-
guishable past from present or future. It was not as easy
for thinkers. In ancient and found the first human think-
ing about time. Plato, for example, said that time is the
moving image of eternity. Later, Newton described it as
an absolute, true and mathematical, which runs smoothly.
In the twenties of last century, Einstein came to regard as
a mere illusion. These ideas reflect the immense com-
plexity of the time, an issue that has been the subject of
reflection for many philosophers and research for many
scientists. Scientists are precisely those who now seek to
address the fact that science does not provide a clear
definition of what is time.
The only fundamental scientific theory that makes a
preferred direction for time is of the second law of ther-
modynamics, which asserts that the entropy of the Uni-
verse increases as time flows forward. This explanation
provides an orientation, an arrow of time. Our perception
of this would, therefore, a direct consequence of the th-
ermodynamic time arrow.
The entropy of any thermodynamically isolated sys-
tem tends to increase with time and this has to this law a
definite orientation. That the entropy of the universe to
increase over time is that there is a direction, an arrow of
time, a time asymmetry to distinguish past from future,
which corresponds with our own perception of time.
This is clear at the macroscopic level, however, on a
microscopic scale, since the amount of energy involved
in the process is so small, it is more difficult to assert
that entropy is increasing, and that therefore time is
moving forward (toward the future), rather than back-
ward (toward the past).
In the macroscopic world, how can we explain the
obvious time-asymmetry of the universe if the funda-
mental laws of physic are time-symmetric? Physicists
usually answer this question first observing that, if the
initial state of the universe would be an equilibrium state,
the universe will remain for ever in such state, making
impossible to find any time-asymmetry.
The set of irreversible processes that began in an un-
stable non-equilibrium state constitute a branch system
[1,2]. That is to say, every one of these processes began
in a non-equilibrium state, which state was produced by
a previous process of the set.
Once I have understood the origin of the initial un-
stable state of each irreversible process within the uni-
verse it is not difficult to obtain a growing entropy, in
any subsystem within the universe. Alternatively, taking
into account the enormous amount of information con-
tained in the subsystem we can neglect some part of it
[3,4]. I can use more refined mathematical tools [5,6].
With any one of these tools I can solve this problem.
It remains only one problem: why the universe began
in an unstable low-entropy state? If I exclude a miracu-
lous act of creation we have only three scientific answer:
a) The unstable initial state of the universe is a law of
b) This state was produced by a fluctuation.
c) The expansion of the universe (coupled to the nu-
clear reactions in it) produces a decreasing of the (mat-
ter-radiation) entropy gap.
The third solution was sketched by Paul Davies in ref-
erence [2], only as a qualitative explanation. The expan-
R.O. Aquilano / Journal of Bioph ysic al Ch emistry 2 (2011) 49-52
Copyright © 2011 SciRes. Openly accessible at http://www.scirp.org/ journal/JBPC/
sion of the universe is like an external agency (namely:
external to the matter-radiation system of the universe)
that produces a decreasing of its entropy gap, with re-
spect to de maximal possible entropy, max
S (and there-
fore an unstable state), not only at t = 0 but in a long
period of the universe evolution. We shall call this dif-
ference the entropy gap ΔS, so the actual entropy will be
SS S.
In the microscopic world Feng and Crooks created a
method to accurately measure the time asymmetry of the
microscopic. In fact have found that, on a microscopic
scale and for some intervals, entropy can actually de-
crease. And that while the general entropy increase on
average, each time the experiment does not, that is, time
is not always a clear direction. My work aims at under-
standing the relation between time asymmetry and en-
tropy, which would also be crucial for the development
of future molecular and cellular studies.
We know that the universe isotropic and homogeneous
expansion is a reversible process with constant entropy
[7]. The matter and the radiation of the universe are in a
thermic equilibrium state *()t
at any time t. As the
radiation is the only important component, from the
thermodynamical point of view, we can chose *()t
as a black-body radiation state.
Let us consider an isotropic and homogeneous model
of universe with radius a. From the conservation of the
energy-momentum tensor and radiation state equation,
we know that -1
aT, we can verify that S const.
The irreversible nature of the universe evolution is
not produced by the universe expansion, even if ρ
has a slow time variation. Therefore, the main
process that has an irreversible nature after decoupling
time is the burning of unstable H in the stars (that pro-
duces He and, after a chain of nuclear reactions, Fe).
This nuclear reaction process has certain mean life-time
and phenomenologically we can say the state
of the universe, at time t, is:
()()0[() ]
tte t
 
  (1)
where 1
is certain phenomenological coefficient
constant in time, since all the time variation of nuclear
reactions is embodied in the exponential law t
. I can
foresee, also on phenomenological grounds, that 1
must peak strongly around 1
the characteristic en-
ergy of the nuclear process.
All these reasonable phenomenological facts can also
be explained theoretically: Eq.1 can be computed with
the theory of paper [9] or with rigged Hilbert space the-
ory [5]. In reference [10] it is explicitly proved that 1
peaks strongly at the energy 1
. The normalization
conditions at any time t yields:
()() 1,...0tr ttrttr
 (2)
The last equations show that 1
is not a state but
only the coefficients of a correction around the equilib-
rium state *()t
. It is explicitly proved in paper [10],
that 1
has a vanishing trace.
I am now able to compute the entropy gap S
respect to the equilibrium state *()t
at any time t. It
will be the conditional entropy of the state ()t
respect to the equilibrium state *()t
[ log()]Str
 (3)
Using now Eq.1, and considering only times
I can expand the logarithm to obtain:
 (4)
where I have used Eq.2. I can now introduce the equilib-
rium state i for T
. Then:
13 2
 (5)
where et
is a diagonal matrix with this function as
diagonal. But as 1
is peaked around 1
we arrive to
a final formula for the entropy gap:
 (6)
where C is a positive constant.
I have computed of S
for times larger than decoup-
ling time and therefore, as 2/3
at and 1
where t0 is the age of the universe and T0 the present
temperature. Then:
 (7)
where C1 is a positive constant. The curve ()St it has
a maximum at 1
and a minimum at 2
tt. Let us
compute these critical times. The time derivative of the
entropy reads:
St S
tT t
 
This equation shows two antagonic effects. The uni-
verse expansion effect is embodied in the second and
third terms in the square brackets an external agency to
the matter-radiation system such that, if we neglect the
second term, it tries to increase the entropy gap and,
therefore, to take the system away from equilibrium (as
we will see the second term is practically negligible). On
the other hand, the nuclear reactions embodied in the
R.O. Aquilano / Journal of Biophysical Chemistry 2 (2011) 49-52
Copyright © 2011 SciRes. Openly accessible at http://www.scirp.org/ journal/JBPC/
y-term, try to convey the matter-radiation system to-
wards equilibrium. These effects become equal at the
critical times tcr such that:
cr cr
For almost any reasonable numerical values this equa-
tion has two positive roots: 12
0cr cr
ttt .
For the first root we can neglect the y 0
tterm and I
(this quantity, with minus sign, gives the third unphysi-
cal root).
And for the second root I can neglect the
2( /)
tt term, and I find:
If I chose appropriate numerical values we can see
that it probably produces also a growing order, and
therefore the creation of structures like clusters, galax-
ies and stars [12].
Also I have a growing of entropy, a decreasing order
and a spreading of the structures: stars energy is spread
in the universe, which ends in a thermic equilibrium
[13]. In fact, when t the entropy gap vanishes
(see Eq.7) and the universe reaches a thermic equilib-
rium final state.
Since 414
101.5 10t years after the big-bang all
the stars will exhaust their fuel [13], so the border be-
tween the two periods most likely have this order of
magnitude and must also be smaller than this number.
This is precisely the result of our calculations.
In the molecular world, we can associate this with the
stem cells, seeing that the gap of entropy is close to
zero or zero. Feng and Crooks [14] contributed to de-
veloping a measure of the time-asymmetry of recent
single molecule RNA unfolding experiments.
With the previous calculations but consistent with the
body temperatures of animals, we see that the equations
are reduced almost naturally to zero entropy, and spread
over time, reaching the level of Feng and Crook, pro-
ducing the possibility that this occurs also mentioned
that the cells could become immortal.
We see that nature, at the macroscopic level, has a ten-
dency to mess up, which in physics called entropy effect.
However, on a microscopic scale, since the amount of
energy involved in the processes is very small, it is very
difficult to say that entropy is increasing, and therefore
time to move forward rather than backward.
Feng and Crooks say have a method to accurately
measure time asymmetry at the microscopic level. They
found that during some intervals the entropy may de-
crease. And, although the overall entropy increases at
each moment of the experiment does not, then the time
has no clear direction and time asymmetry is not secured,
but time has a symmetrical (not unlike this past or fu-
ture). As time progresses in the macroscopic world, it is
unclear at the level of a single molecule, and if we asso-
ciate this phenomenon to stem cells, as these remain
unchanged we could say that would be the only natural
case of detention of the arrow of time, which could be
associated with natural perennial or cell immortality.
I wish to thank to Jack Szostak of Howard Hughes Medical Institute
to fruitful discussions. This work was supported by grant of National
University of Rosario (UNR), PID 1ING198.
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