1.6 Closed and Open Systems

An isolated closed system exchanges neither energy, matter, nor information with its environment. Because of the Second Law of Thermodynamics, such a closed system may start away from equilibrium but will always tend down its energy gradients to a final resting state of thermodynamic equilibrium. A fraction of the energy is always irreversibly transformed into heat, which is a measure of the degree of randomness of the motion of molecules. Rudolf Clausius in the 1850s introduced the concept of entropy as a measure of the irreversibility of physico-chemical processes as they proceed towards a state of equilibrium. The concepts of energy conversion proposed by James Prescott Joule in 1845¹, and heat propagation proposed by Jean-Baptiste Joseph Fourier in 1822², led William Thomson, Lord Kelvin to formulate a new principle: the existence of a universal tendency towards degradation of mechanical energy into thermal energy, with a consequent increase in entropy.

Critically, the Second Law of Thermodynamics introduces an ‘arrow of time³‘, with its associated irreversibility. This was not implicit in the Newtonian system of mechanics where time was reversible. 

In the late 1800s, James Clerk Maxwell and Ludwig Boltzmann developed a theory to describe the physical properties of gasses by treating a gas as a huge assembly of molecules in ceaseless random motion, continuously colliding with each other and with the walls of the container with maximal randomness (disorder). The temperature of the gas was related to the level of motion of the particles. This view of gases reduces the problem of temperature to a problem of motion dynamics based on the Newtonian dynamics. In 1872, Boltzmann expressed entropy as a measure of molecular disorder by this method of Statistical Mechanics which equated temperature and microscopic events as the result of mechanisms still based on interaction of molecules^{4 5}. Thus, in a closed system entropy is bound to increase to its maximum and is associated with total disorder of its molecular elements. 

There is consensus that the universe is highly heterogeneous and far from equilibrium. If the universe were to be considered as a closed system, then, according to physicist Hermann von Helmholtz, it would be doomed to evolve towards a so-called ‘heat-death’, with total randomness of its elements. 

In contrast with a closed system, an open system is still limited by some boundaries, but it exchanges energy and matter with its environment. 

How order can emerge from disorder, even in inorganic open systems, is demonstrated well by the formation of convections cells in a simple open system of a container in which a liquid is heated. Before boiling, the liquid becomes organised as geometrical metastable structures of approximately regular right hexagonal prisms, a phenomenon described by Henry Bénard in 1900, and hence called ‘Bénard Cells‘. Such convection patterns are good examples of structures that are self-organised, with microscopic random movements spontaneously becoming ordered at a macroscopic level. The inorganic world is full of such transient dynamic ordered structures.⁶

More recently, and even more dramatically, spontaneous chemical reactions observable in a Petri dish opened a very fruitful field with the discovery of spontaneous chemical oscillations in a closed system. According to the laws of chemical reactions, such reactions are expected to follow a gradient to their final chemical equilibrium⁷. However, a simple reaction mixture of cerium ions that catalyse the oxidation of malonic acid by bromate and water in a Petri dish behave quite differently. Unlike most familiar chemical reactions, this one oscillates changing from yellow to colourless and back again to yellow twice a minute instead to going directly to equilibrium. This phenomenon was discovered in the late 50s by Boris Belousov, a Russian chemist, during the Cold War. However, his colleagues in Russia were mostly unreceptive to his unexpected observation. Contact with the West was limited at the time and Western scientists also were sceptical of such claims. Belousov abandoned science because of this. It took another ten years for convincing experiments to be published in the leading international journal Nature by his younger Russian colleague, Anatol Zhabotinsky.⁸ That work opened the door to the world of chemical reactions named after Belousov and Zhabotinsky: ‘BZ Reactions‘⁹. 

The amounts of substances formed in BZ reactions oscillate and, following the rules of Chaos Theory, generate bifurcating regions of periodic oscillations (order) alternating with regions of aperiodic oscillations (chaos). These chemical reactions give rise to a geometrical distribution of chemical products which generate unexpected spatio-temporal patterns of travelling concentric and spiral waves. The geometrical patterns of these chemical reactions indicate that the molecules show some spatial order. These oscillating patterns are still part of a closed system with no new chemicals added as the process moves towards its final equilibrium: the BZ reactions in a Petri dish eventually come to a rest, with completely random distribution of the molecules (maximal entropy) and loss of any spatio-temporal pattern, as predicted by the Second Law of Thermodynamics. 

The mathematical description of the BZ reactions involves reaction-diffusion equations which describe any system involving constituents that are locally transformed by reactions and coupled to neighbouring sites by diffusion. Reaction-diffusion equations represent a prototype model of pattern formation for traveling waves, spiral waves, concentric waves, and more. We will see that processes involving reaction-diffusion reactions abound in nature, particularly in living systems. 

---

1. Click here to read Joule’s original article in Philosophical Magazine. 3. 27 (179): 205–207. 1845. ↩︎
2. Jospeh Fourier (1822): Théorie analytique de la chaleur. Firmin Didot Père et Fils. Click here to read a facsimile of the original French edition. ↩︎
3. This concept was developed by Sir Arthur Eddington in 1927. See also: https://en.wikipedia.org/wiki/Entropy_as_an_arrow_of_time ↩︎
4. See https://plato.stanford.edu/entries/statphys-Boltzmann/#3.1; ↩︎
5. These concepts also led to the development of Information Theory by Claude Shannon. ↩︎
6. Study of such structures includes the field of Synergetics, developed by Hermann Hakan in the 1960s. ↩︎
7. “In a chemical reaction, chemical equilibrium is the state in which both the reactants and products are present in concentrations which have no further tendency to change with time, so that there is no observable change in the properties of the system.” https://en.wikipedia.org/wiki/Chemical_equilibrium ↩︎
8. AN Zaikin & AM Zhabotinsky (1970): Concentration wave propagation in a two-dimensional, liquid-phase self oscillating system, Nature, 225; 535-537. ↩︎
9. See more at: http://www.scholarpedia.org/article/Belousov-Zhabotinsky_reaction ↩︎

---