# Of entropy, and the stripper across town

## The subject of physics was very interesting to me in high school because I could relate what I was studying in physics with events in my daily life: various kinds of motion, boiling and freezing of water, generation and propagation of sound, colours in a rainbow, operation of a light bulb and so on.

The subject of physics was very interesting to me in high school because I could relate what I was studying in physics with events in my daily life: various kinds of motion, boiling and freezing of water, generation and propagation of sound, colours in a rainbow, operation of a light bulb and so on. When I entered Presidency College as a physics honours student, one of the subjects in our first year’s curriculum was thermodynamics.

In this course, I encountered for the first time in my life a totally abstract concept: that of entropy. It was abstract because I could not point to any specific property of any object which I could measure, perhaps with a very sophisticated instrument in the physics lab and say that its entropy was of a certain amount. Entropy was defined only by a mathematical formula; an incremental change in entropy of a substance was an incremental increase in its amount of heat divided by its absolute temperature. Remarkably this entity had all kinds of implications in the transformation of heat energy into work, even though we could not quite define it in words.

There was a somewhat vague interpretation of entropy though. Entropy of a system was supposed to be a measure of disorder or “randomness” in the system. Although this statement was never “proved” and therefore had to be taken for granted by our faith in physics, it added to the mystique of the concept of entropy; the concept of “disorder” was equally fascinating and did not seem to be directly connected to heat transfer. Typically, many students of physics and engineering lose interest in the subject of thermodynamics at this point. They would only want to learn how to solve certain problems in a mechanical way, following examples in the book.

They do not find it worthwhile to spend their time pondering the concept and debating its significance with their classmates. We owe it to our professor, Shyamal Sengupta (SS) at Presidency College, for generating an intrigue about entropy. SS had a personality which could be described as a combination of a poet and a philosopher. He introduced the concept of entropy to us in a way that suggested it was from another world. It almost seemed like understanding entropy was a little bit like understanding God! I believe that his teaching had a profound impact on his students which no one fully appreciated at the time.

It made us realize that we belonged to a special group; a group which had the ability to go beyond the obvious and the ability to think about and appreciate the brilliant abstract concepts that physics offered. It also forced us to explore our own full potential in this respect and prepared us for more abstract and difficult concepts to come later in our studies, especially those of the theory of relativity and quantum mechanics. Appreciating entropy was the first test in separating the “men” from the “boys”, so to speak: the ones who were intellectually sophisticated enough to pursue the mysteries of the universe from the ones who were studying physics just to get a college degree and a job.

There was a silent understanding among the members of the first group about this and this realization also provided a life-long unifying force among them! They developed the belief that only their classmates who shared their passion about entropy would be the ones who could truly understand them. The concept of entropy shook up our brain cells and enhanced our confidence. As abstract as the concept of entropy was the second law of thermodynamics, which stated that the entropy of the universe could never decrease! What does it even mean when you have difficulty in grasping the meaning of entropy in the first place? If nothing else, it made us think beyond anything we had learned up to that point in our education. It was also amazing how many different interpretations existed for the concept of entropy and in how many ways the second law of thermodynamics could be formulated.

It was a formidable task just to understand that these different formulations were indeed equivalent. One of my college friends once jokingly asked me: “Basab, do you lose sleep worrying that the entropy of the universe is continuing to increase every second?” It sounds almost as bad as the increase in population on this earth or increase of carbon dioxide in the atmosphere; but is there something really alarming about ever increasing entropy? Would the earth cease to function normally if the total entropy exceeded a certain threshold? Could it be that global warming or nuclear disasters such as the ones in Fukushima are somehow a consequence of this law?

The argument could be made that if we could convert heat energy directly into work with one hundred per cent efficiency, something the second law of thermodynamics precludes, we would have no exhaust gasses full of carbon dioxide or “spent” nuclear rods lying around in a nuclear plant. On a more intellectual level, since the second law of thermodynamics is not symmetric with respect to direction of time, it has been proposed to supply an explanation of the difference between moving forward and backwards in time, such as why the cause precedes the effect (the causal arrow of time). Perhaps there is something even more profound about this law. Perhaps it is only a special case of a much more universal principle which applies not only to the inert objects that physics deals with, but also to living objects. We can easily correlate the law with the fact that it is easier to create clutter than order. Perhaps it also implies that it is easier to be noisy and chaotic than calm and quiet and it is easier to hate than love.

I am also fascinated by the term “entropy” because I find myself entrapped in the concept! It is such an exotic name and unlike almost all other terms used in physics, such as force, energy, work, power, inertia, resistance, current, pressure etc., it has no usage in our everyday language. Apparently, the name “entropy” was coined by the German physicist Rudolf Clausius from the Greek word “tropos” which means “transformation”. Clearly the transformation involved here is the transformation of heat into work. When I was teaching a freshman level introductory physics course after my PhD, I had occasional discussions with a colleague of mine, who was also teaching the same course, about how to make the course more interesting to the students and we both agreed that interjection of humour would be appropriate.

He told me that, in one of his tests with multiple choice answers, one of the questions was “What is entropy?” As possible answers he included: a) Amount of heat in a system; b) Measure of disorder of a system; c) Measure of temperature of a system and d) Name of a stripper downtown. When I thought about his last answer, I felt that it was probably not a far-fetched idea to think of a seductive temptress as an embodiment of entropy. She mesmerized us, appeared before us in a variety of different ways, dared us to explore her, prepared us for future interactions with damsels like her and most importantly, separated the men from the boys!

(The writer, a physicist who has worked in industry and academia, is a Bengali settled in America.)