Entropy: A Story of Science as Art – by Ashwin Vaidya

A recent informal discussion with my students on the nature of creativity in the sciences revealed that, for them, creativity is housed primarily in the arts. But don’t scientists also create, muse, imagine, and entertain…as much as artists experiment, observe, measure, analyze, and posit?

As I re-read The Two Cultures by C.P. Snow recently, I was struck by his famous observation regarding the schism between the arts and sciences and the lack of understanding of one another’s disciplines:

A good many times I have been present at gatherings of people who, by the standards of the traditional culture, are thought highly educated and who have with considerable gusto been expressing their incredulity at the illiteracy of scientists. Once or twice I have been provoked and have asked the company how many of them could describe the Second Law of Thermodynamics. The response was cold: it was also negative. Yet I was asking something which is about the scientific equivalent of: ‘Have you read a work of Shakespeare’s? [1]

Thermodynamics and its relationship to pattern formation in fluid mechanics has become my newfound research passion. As a physicist, I will use this blogging opportunity, collegially provided to me by The Creative Research Center, to redress the situation that Snow refers to, and ‘educate’ my colleagues in the arts and humanities about the second law of thermodynamics, in the best way I understand it.

A story of physics told through the unraveling of the second law of thermodynamics sheds new light on the natural interplay of science, humanities and arts in our daily lives; it reveals the scientific enterprise as a creative and democratic endeavour, and the artistic process as being rigourous and having a method of its own.

What I have found, to my amazement, is how fundamental a subject thermodynamics is. The study of heat and energy is only a little more than a century-and-half old and is slowly being recognized as a causal principle behind several aspects of nature (such as the patterns on a butterfly), the life cycle (several functional aspects of a cell) and the process of evolution as a whole[2].

In particular, the second law of thermodynamics, which introduces the idea of entropy, has come to occupy a special place in the vast literature of fundamental physics, as the only concept in physics to hint at a meaning of ‘time’. Most branches of physics treat time as a reversible parameter; thermodynamics is the only branch to account for nature’s inherent irreversibility, which has become the scientific definition of time.

One exact statement of this law according to Clausius (there are a few more equivalent popular versions via Lord Kelvin, Constantin Caratheodory and others) goes: The entropy of the universe tends to a maximum. [3]

To understand this statement would require a clear understanding of the idea of entropy. There is no consensus on the definition; it has come to mean one or many of the following: disorder, wasted energy, dispersed energy, or dissipation.

For the purposes of this discussion, let us adopt a simple and popular definition (without the accompanying nuances) of entropy as unusable energy. The first law of thermodynamics states that the total energy in the universe is a constant, but can be can be converted from one form to another. From this standpoint, the second law points out that although the net amount of energy does not change, the amount of unusable energy is increasing over time until at some point all available energy in the system is unusable. Physicists before and since Snow have laid great faith in the immutability of this law, eliciting the famous comment by Sir Arthur Eddington:

If someone points out to you that your pet theory of the universe is in disagreement with Maxwell’s equations – then so much worse for Maxwell’s equations… But if your theory is found to be against the second law of thermodynamics I can give you no hope; there is nothing for it but to collapse in deepest humiliation. [4]

I would further like to point out that the second law has parallels in eastern philosophy.

As Krishna enlightens Arjuna, the warrior, on the eve of the epic battle of Mahabharatha (described in the ancient Indian philosophical treatise, ‘Bhavagad Gita’), on the meaning of life, he points to the fundamental and conserved (or constant) qualities of nature (within both individuals and the collective universe) called ‘gunas’ in Sanskrit. In chapter 14 of the Bhagavad Gita, Krishna states, referring to the nature of humanity:

Sattva or goodness; Rajas or activity and Tamas or inertia; these three gunas of mind bind the imperishable soul to the body…[5]

The three gunas are however described as a fundamental embodiment of all of nature, including matter, consciousness and the realm of energy beyond. This statement, and its detailed ensuing description in the Gita, has remarkable similarities to the detailed mathematical formulation of the second law.

While the traditional scientific definition of entropy is anthropocentricand hence the common connotation of the second law rather negative, the above metaphysical parallel of this law (if so interpreted) is devoid of this human bias and regards the return to nature as a desirable trait.

The second law, since the time of Snow, has spread its influence and exposed parallel notions beyond physics by pervading the disciplines of ecology, chemistry, biology, environmental sciences and even economics. In his book Entropy: A New World View, Jeremy Rifkin[6], an economist and political thinker, gives a remarkable account of how the concept of entropy has captured the imagination in science and the humanities. In considering how entropy and the second law play a fundamental role in our daily lives, Rifkin helps uncover a more revealing definition and fundamental role of entropy than the focused scientific definitions. The creative evolution of this idea (not always called ‘entropy’ or defined by the ‘second law of thermodynamics’) is perhaps a very simple but telling example about it. Perhaps Snow was a little hasty in his comments by not realizing that entropy by many other names can ‘smell’ sweeter.

While we have simply dwelled on the meaning of entropy above (and tersely at that), the ongoing consequences of the idea are crucially more important. As the world tumbles hopelessly toward environmental catastrophe, a greater public understanding of the lessons of entropy is essential.

We cannot hope to solve a problem of this magnitude all on our own. A better understanding of each other’s disciplines will help foster stronger collaborations between artists and scientists, and open new pathways and solutions – ones yet to be imagined.

Severus Sebokht, the Syrian bishop, thought it necessary to state the obvious in 662 AD: There are also others who know something.

Perhaps it is time to state the obvious yet again.

References

1. C.P. Snow, The Two Cultures. Cambridge: Cambridge University Press, 1959
2. Frijitof Capra, The Web of Life: A New Scientific Understanding of Living Systems, Anchor, 1997.
3. Kondepudi, D., Introduction to Modern Thermodynamics, Wiley, 2008.
4. Arthur Eddington, The Nature of the Physical World, University of Michigan Press; 4th prtg, 1981.
5. www.santosha.com/philosophy/gita-chapter14.html [An English Translation of the Bhagavad Gita].
6. Jeremy Rifkin, Entropy: A New World View, Bantam Books, 1981.

— Ashwin Vaidya, PhD, is an Assistant Professor in the Department of Mathematical Sciences in the College of Science and Mathematics at Montclair State University, faculty advisor to the Physics and Art Photography Competition, and a dynamic interdisciplinary contributor to the inquisitive conversations of The Creative Research Center. Beyond his restless examinations of the interpenetration of the arts and sciences, Dr. Vaidya’s research interests lie in the areas of Applied Mathematics, Mathematical Fluid Mechanics, Non-Linear Partial Differential Equations, Hydrodynamic Stability, Non-Newtonian Fluid Mechanics, Fluid-Structure Interaction, Experimental Fluid Mechanics and Philosophy of Science. For his doctoral thesis, he worked on problems concerning the steady state behavior of rigid bodies sedimenting in Newtonian and non-Newtonian fluids. He is, in general, interested in problems concerning fluid structure interactions and non-Newtonian fluid flow and their implications in as diverse fields as geophysics, environmental fluid mechanics and biofluid mechanics.