Entropy - and Everything Else

Entropy is the most cumbersome term in science – leading to some confusing interpretations at times – but the law associated with this term is very important, and has attracted scientists and enthusiasts across disciplines – from basic and applied sciences to the aspects of social science. The term – coined by German physicist Rudolf Clausius (1822 – 1888) is enshrined in the 2nd Law of Thermodynamics. As with all accepted theories or laws of Nature, one law must agree with others to satisfy their compatibilities (compatibility theory) – which mean that the 2nd law must agree with the other laws of thermodynamics – the 0th, 1st, and the 3rd. Therefore this piece will briefly highlight the other three laws prior to embarking on explaining the 2nd law – to show its applications and implications in simple and easily understandable terms – at the same time weaving some traces of metaphysics into it. But before that, meanings of some terms must be delved into by revisiting Physics 101 – because these terms are crucial for understanding the laws.

SYSTEM. A system is a collection of objects (or could even be one object if one considers the molecular activities within that object) and the interactive processes within. It is selected, for the convenience of description and analysis – as an entity defined by its boundaries through which it interacts with the surroundings. The surroundings can be other systems, or generally the environment. The system and its surroundings are collectively referred to as the universe (we hear about this term often in astronomical contexts). Generally, a system – an open system interacts with its surroundings by freely or spontaneously exchanging (receiving and giving) matter and energy. A closed system exchanges only the energy with its surroundings. An isolated system, mostly manufactured – exchanges neither matter nor energy with its surroundings. One can define semi-enclosed, semi-isolated or other systems depending on the limit, restriction or filtration one applies on the exchange of energy, matter, or both. Also important is the state – it refers to the condition of a system in time – defined and measured in thermodynamics by temperature, pressure and density (mass and volume) – but generally refers to the condition of energy.

ENERGY, WORK AND HEAT. Energy is the ability of a system to do work. Work is done by transferring energy when a system is enacted by a force. Force refers to the application of external energy to cause accelerating motion on a system. The terms energy and work are equivalent, and both represent scalar quantities (magnitude only), while force is a vector term (with both magnitude and direction). There are different forms of energy: potential (stored energy in a system that has the potential to do work when released); kinetic (energy of a working system due to its motion); internal (total energy contained in a system; and any change of it, is the difference between heat or energy transferred into the system and work done by the system).

Heat refers to the internal energy in a system that is transferable to its surroundings when a temperature gradient exists (e.g. one way spontaneously, from hot to cold). Enthalpy is defined as the system’s internal energy plus the energy imparted by works done on its volume by external pressures. Temperature is the measure of average internal energy in a system. In SI system, the unit of force is Newton (kg.m/s^2), and the unit of energy, heat and enthalpy is Joule (J = N.m = kg.m.m/s^2). The rate of doing work or transferring energy is power, given in Watt (W = J/s). Temperature is measured in the thermodynamic Kelvin (in honor of British physicist WT Kelvin, 1824 – 1907) scale with absolute zero defined at K = -273.16oC (C = Celsius, in honor of Swedish astronomer A Celsius, 1701 - 1744). At absolute zero, all activities stop from micro to the macro level, therefore at this stage they are all immeasurable.

A few words on the processes involving the transfer of matter and energy. One of them is spontaneous – referring to the process that occurs on its own, without requiring an external energy input or work – this process is driven by downslope gradient. In the domain of physical processes, spontaneity is synonymous with the works of ubiquitous gravitational force – in the capacity of Natural downslope restoration and balancing acts. A work process takes place when an external force is applied to displace a system against an upslope gradient (e.g. against gravity). Thermal processes of heat exchange are four types – adiabatic (no transfer of heat across boundaries); isothermal (constant temperature); isobaric (constant pressure); and isochoric (constant volume). Equilibrium refers to the perfect balance of all processes in a system – at this state no spontaneous exchange of energy and matter takes place with the surrounding. Further, as we shall see – most of the processes in the systems of Nature (also in Social Systems) are Reversible. This process says that if some works are done to such a system (without reaching the breaking point of failure) – it will work out by itself (or when external energy is infused) – to revert back to its initial stage (albeit, may never recover fully in the contexts of space and time). In Engineering literature such systems are termed as an Elastic System. However repeated work attempts on such systems, affect it by pushing toward the stage of irreversibility – by a process known as Fatigue. There are some other systems of Nature that only works One-way – they are the ones recognized as Irreversible or Plastic processes. The 1st and the 2nd Laws of Thermodynamics explain how these two contrasting processes define things.
  
​LAWS OF THERMODYNAMICS. Thermodynamics is the study of the effects of work, heat and energy on a system in the domain of Thermodynamic Force Field (TDFF).

• The 0th Law is the law of thermal equilibrium. It says that if two systems are in thermal equilibrium with a third system, then the two are in thermal equilibrium with each other. This law is not universal because it fails when applied to social and international relations – for example, if two individuals A and B are friends with a third individual C, then A and B are not necessarily friends with each other.
  
• The 1st Law is the most widely known law – and it is intuitively very clear. In thermodynamic literature, it is worded as: the change in internal energy of a system is equal to the heat added to the system minus the work done by the system. The most familiar form of this law is the conservation of energy – that energy can neither be created nor destroyed – it can only change from one form to another. This law is universal representing reversibility of processes, and has given birth to several familiar names such as: carbon cycle, hydrologic cycle, life cycle, etc.
  
• The 3rd Law is the law of absolute minimum thermal energy – the entropy of a system approaches zero as the temperature approaches absolute zero.
  

ENTROPY AND THE 2ND LAW. Having clarified all the terms, it is time now to understand entropy and the 2nd law. Entropy is the change in the state of energy (ΔS) of a system during transformation. In thermodynamics, this change in the state of energy (from initial to the final, or from one level to the next) divided by the temperature (in Kelvin scale) at which change occurs, is the measure of entropy (J/K). Before going further, let us attempt to see some major states of energy transformation – some in the arena of coastal processes. What are these? Some familiar examples are:

• the birth of a plant or life; at this state, time starts for that particular plant or life
  
• the demise of a plant or life
  
• the spectacular metamorphoses of dragon flies, moths and butterflies from larvae to adulthood
  
• the frictional dissipation of mechanical and physical energies into heat
• the breaking of a wave
• the breaking of long waves – tsunamis and storm surges on way to forceful flooding

Each of these examples represents an irreversible process. However, if one looks closely within all these major transformations, one would find many micro- or small-scale transformations, which are not necessarily irreversible. I will attempt to explain why so.

The 2nd law states that entropy of the universe does not change in a reversible process (ΔS = 0), but it always increases in an irreversible process (ΔS > 0). This means that in a reversible process there are continuous and spontaneous exchanges among the systems of the universe that aim to achieve equilibrium – therefore the net change in entropy is zero. It indicates that if the entropy of a system decreases (ΔS < 0), the entropy of the surroundings must increase (ΔS > 0) by the same amount – so that the total entropy of the universe remains unaffected. This is indeed the restatement of the 1st law.

But the second part of the law – dealing with the irreversibility of processes is intriguing – in a sense that it adds a twisted but essential qualification to the 1st law. The twist is added in the form of turning a scalar entropy (like energy) into a vector quantity by assigning the sense of irreversible directionality. To understand the second part let us consider two simple examples:

1. A system spontaneously radiating out heat in time to become colder – like a hot rod kept in the open. In this case, the entropy of the surrounding is increased by receiving heat from the rod. It is an irreversible process because heat cannot flow spontaneously from a cold system to a hotter one. It indicates something very interesting – and it is the arrow of time. Let us examine it further. Our Sun is a very hot object – and the Earth as a colder planet, receives part of that radiating heat from the Sun. The colder Earth cannot give the heat (although it does radiate back some to the colder atmosphere) it receives back to the Sun. The result is that the entropy of our Earth is continuously increasing over time. What happens to all the increased entropies? Well, many of Earth’s processes are reversible – therefore the gained entropies get recycled in different forms – one such familiar major process is fossilization of energy over time – like oil, gas and coal deposits.         
   
2. In another example: an ice cream melts by gaining heat from the surrounding. This is again an irreversible process. But let us explain it in terms of order and disorder. The ice cream – a system of higher order becomes disordered (a mess of melted nuisance) by gaining heat. Therefore disorderliness is an indication of randomness and high entropy. It is somewhat like Murphy’s (EA Murphy Jr. 1918 – 1990) law: anything that can go wrong will go wrong. Now, if we go back to our example of the Sun-Earth universe, the Earth as a cold system (like the ice cream) is not only getting enriched by gaining entropy from the Sun, but the 2nd law says it is also getting continuously disordered. Let us examine the aspects of disorderliness further:

• What does it mean that the Earth is getting disordered in time? The answer to this question lies in defining Earth. As already pointed out earlier, many of Earth’s processes are reversible – and the Earth that we know today and many of its processes are manufactured – therefore some disorderliness is restored back or is given a different dimension by doing work – additionally some are getting recycled in different forms. But imagine a piece of Earth that is well-built and ordered – if we leave that place without touching it further – it will deteriorate and disappear to nothingness – the 2nd law in action – and we call it Nature or the law of Nature. However, there is an element of subjectivity there – because what humans consider as deterioration to nothingness – is the gain for other lives.        
• What do the examples of irreversibility imply? If we examine closely, the examples say that to stop irreversibility, work has to be done. The hot rod or the cold ice cream can be isolated, for example, by a manufactured device (e.g. a thermos for the hot rod, and a freezer for the ice cream). In both the cases, work is done through the manufacturing process, to stop the irreversibility of process. But what about the Sun-Earth system? Well, its scale is so overwhelmingly huge that – it forms Nature, thus defining the arrow of time and disorderliness.           

The arrow of time in one direction and the inescapable growing disorderliness or higher entropy (another easily understandable term for this one-way Natural process is aging or burning out of all entities in time) in irreversible processes needs a close interpretive look. Because if one tries to explain things of a Natural system, let us say, in short time-scales – these two realities defined by the 2nd of law of thermodynamics may not have straightforward fit – rather one will be inclined to note that Natural irreversibility is not what it seems.  Let us attempt to understand this assertion:

• Time: Scientists say that time (let us say absolute time) started with the Big Bang – some 13.8 billion years ago. The theory says that this episode gave birth to the ever expanding universe – thus the arrow of time – with our solar system coming into existence some 9.3 billion years after that.  But human perception of time is not always one way – it is rather relative or subjective. Let us examine it in the light of a piece on TIME posted on this page at an earlier occasion. If one looks into a long period of time – it certainly looks like a straightforward-heading arrow – but if broken down into small pieces, one may see kinks in the arrow of time. These kinks are due to the dynamic equilibrium or reversibility of processes within the irreversible arrow of time. Some simple examples are: years pass by – but within each year the Earth’s orbital motion around the Sun repeats, giving rise to seasons. And within each day, the Earth spins on its own axis, giving birth to the repetitions of day-light and dark-night. Or the repetitions of glacial-interglacial periods that occurred over geologic time in the history of Earth.    
  
• Disorderliness: Similarly, the definitions of order and disorder can also be interpreted in terms of relativity or subjectivity. Within the process of order to disorder – one can find several episodes of attempts to restore order – from asymmetry to the symmetry of dynamic equilibrium. It is just the characteristic signature of The Fluidity of Nature. Here again, the disorderliness fate of an irreversible process is interrupted by some reversibility attempts.   
• Life: Let us examine the arrow of time and disorderliness in the context of life. The wheel of life revolves around: birth-growth-decay-demise and birth again. The 1st law of thermodynamics in action – that energy flows from one state and form to another transforming the phase of life in the process. If one looks at a particular life, from end to end, the arrow of time and disorderliness are clear. But birth to growth of positive phase is not same as the negative phase of decay and demise. And interventions in terms of therapeutic doses of medicinal treatments (manufactured) add kinks to the life-process.
• The General Theory of Relativity GTR: GTR and its subsequent modification of the governing field equations to accommodate the observations of the expanding universe – leading to the birth of Big Bang Theory (see more in Einstein’s Unruly Hair) – indicate something interesting in the light of 2nd Law of Thermodynamics. The expanding universe after the Bang as a one-way process satisfies this law. But a universe consisting of a system and its surrounding - more appropriately the Multiverse (following the term coined by W James in 1895) - must head toward attaining dynamic equilibrium – because they are always complementary. The existence of the universe consisting of multiple systems of galaxies governed by the forces of gravitational field waves – implies that the expanding universe after the Bang represents, in all likelihood, a particular state – rather than the ultimate reality. It further implies that Einstein’s Cosmological Constant – may not be a mistake, after all – it just applies to the universe that is destined to attain dynamic equilibrium (within its multiverse setting) at some time – perhaps far, far, far into the future.   
  
• Macro vs. Micro Outlooks: The discussions on the interpretation of time-arrow and disorderliness lead us to discern that the 2nd law of thermodynamics is the reality of macro or large scale irreversible Natural processes in time and space (relatively speaking). But within that, small-scale or micro processes are present that attempt to the reversibility of processes to attain dynamic equilibrium. In the discussed examples of time-arrow and disorderliness, each small-scale process rarely completes the cycle of reversibility – rather each represents a quasi-cyclic process – thus leaving a residual in the direction of time and disorderliness. Thus a residual entropy comes into existence. And the description of multiple residuals in statistical terms yields another dimension to the definition of entropy – the statistical definition. This is similar to the thermodynamic definition: the change in macro-state entropy is equal to the product of a constant (Boltzmann constant {≈ 1.38x10^-23 J/K}; Austrian physicist Ludwig Boltzmann, 1844 – 1906) and the sum of many statistical ensembles of micro-state entropies. 
• Uniqueness of the Hydrologic Cycle: Another interesting example is the well-known hydrologic cycle – that represents an overall reversible balance of riverflow draining into the ocean, and precipitation. But the two modes of balancing acts are fundamentally different – both in space and time. On an annual basis, each of these two modes has separate irreversible characteristics – with the riverflow as a hydrologic wave of one-way flow to the ocean – and the precipitation as a one-way loss of atmospheric moisture.
  
• Let us examine the arguments further by considering a practical example – the coastal erosion in Kerala India, shown in the image (credit: anon). The rate of erosion by whatever Natural causes, may not be there in subsequent years in the same scale – it could be more, may not be there at all, or the coast may build-up. In fact, such quasi-cyclic Natural processes occur in most coastal beaches each year. But over long-term, a trend would appear – for example, continued beach erosion caused by longshore sand transports that occur along many littoral shores around the world. Thus, trend is another interpretation of the arrow of time. 

Let me very brief on the rest of this piece. Depending on what one focuses, the definition of entropy can be stretched and distinguished in terms of major processes responsible for energy flux and transformation. The key to such definitions is to identify a system and its major processes including characterization of them in terms of reversibility, irreversibility or quasi-reversibility (same as quasi-cyclic). And in literature, many different types of entropy were defined and proposed by investigators. For example, S Hawking (1942 – 2018) defined Black Hole Entropy pertaining to the event horizons of the super-gravity mass. Following this argument, the entropy in thermodynamics processes of heat flow can be termed as thermodynamic entropy. One can also define mind-and-matter entropy, biotic entropy, abiotic entropy, etc. In this piece, I like to introduce and define hydrodynamic entropy and socioeconomic entropy. Let me first start with defining hydrodynamic entropy – because that is where my interest lies. In fact, during the developing stage, French physicist NLS Carnot (1796 – 1832; considered the father of thermodynamics) used the downslope water flow analogy (the steeper the downslope energy gradient, the more the power) to understand and define the 2nd law. 
 
COASTAL SYSTEM AND HYDRODYNAMIC ENTROPY. What is hydrodynamic entropy exactly? It is the change in the state of hydrodynamic energy of a system during transformation. Hydrodynamic energies are: potential (proportional to the product of water mass, gravitation acceleration and height above a datum), flow-kinetic (proportional to the product of water mass, and velocity squared), and wave-kinetic (proportional to the product of water mass, gravitational acceleration and wave height squared). Let us assume, for the sake of convenience that hydrodynamics also include sediment transport dynamics of erodible beds – although this aspect can also be defined as a separate system of interest.    

• To describe the coastal systems let me refer back to Civil Engineering on our Seashore on the SCIENCE AND TECHNOLOGY page. The first or the overall coastal system comprises the coastal zone – the area from the oceanward limit of continental shelf break to the landward topographical limit. One can define many sub-systems within this zone depending on the interest of analysis. For example, a harbor is a system with a narrow open inlet and a wide basin inside. It is an open hydrodynamic system – it exchanges matter (both water and sediments) and energies imparted by wave, tide, wind and other episodic events – but the processes are not entirely reversible, because of the presence of asymmetries and residuals.     
  
• The hydrodynamic entropy of a coastal system has heat generation content in it – that occurs through the processes of hydrodynamic energy dissipation as frictional losses at the bottom boundary. This loss represents irreversibility (MKE Planck, 1858 – 1947) – because heat is no longer available to do work within the system. However, in hydrodynamic entropy, frictional loss manifests itself in erosion and transport of bed-materials of an alluvial bed. The friction loss itself says that coastal systems are quasi-reversible.
  
• Thus, the quasi-reversibility in the coastal hydrodynamic entropies is ensured by at least two processes. The first is the asymmetry processes that yield residuals (thus the residual entropy) in the direction of the dominant component. The second is the transformation of alluvial bottom bed through erosion, deposition and sediment transport.
• But, as pointed out earlier at least two coastal processes are irreversible. First is the breaking of a wave – the broken wave cannot be reproduced back into the original wave, but it increases the energy of coastal waters at the beach by raising water levels and giving birth to other processes. Similar is the case of tsunamis and storm surges – both while broken at the coast gives birth to rapid flooding – more vigorous and forceful in tsunamis than storm surges.         

​SOCIOECONOMIC ENTROPY. How do the socioeconomic entropy and 2nd law work? Let me briefly touch on this question. In several pieces on the pages of NATURE and SOCIAL INTERACTIONS, I have highlighted positive and negative social energies. Social energy indicates the accumulation or depletion of societal wealth – wealth in this case refers to the multitude of factors such as economy, social interactions, and favorable degrees of: cohesion/divisiveness, trust/mistrust, integrity/corruption, equality/inequality, peace/disturbance, etc. The nature of these factors is determined by good or bad governance.

The change in the state of societal wealth is socioeconomic entropy. A positive energy is an indication of accumulating wealth, therefore represents good socioeconomic entropy. A bad socioeconomic entropy, on the other hand is a representation of depleting societal wealth. The underlying assumption in such characterizations of the society is that socioeconomy is a reversible process – but in a different interpretation of the term. The reversibility is ensured by the stream of works we put in to sustain socioeconomic progress and growth – and in turning negative into positive. But when a society becomes callous, incompetent and ill-motivated, the positive tends to veer toward the negative. The existence of positives and negatives suggest the reality, that there exist kinks in the character of societal wealth – the kinks are long and short, and high and low. The nature of kinks by itself is an indication of the soundness or weakness of societal wealth.

It ended up being another long piece. I like to finish it with a quote from German Philosopher, Arthur Schopenhauer (1788 – 1860): journalists are like dogs, whenever anything moves they begin to bark. It is like what the Buddha (563 – 483 BCE) - The Tathagata said: it is difficult not to express an opinion about others. And journalists have a loud mouthpiece through the media outlet they serve – therefore it is all the more tempting for them to bark. But as a true and responsible partner of democratic institutions, perhaps it makes sense that journalists and media – make accurate, measured and thoughtful barking for the sake of good socioeconomic entropy. 

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- by Dr. Dilip K. Barua, 18 May 2019

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