Thermodynamic time arrow

Some of you may have heard about the thermodynamic time arrow. Gases escape from open containers and heat flows from a hot body to its colder environment. Never has spontaneous reversal of such processes been observed. We call these irreversible processes. The world is always heading forward in time. Mathematically this is expressed by Clausius theorem. 

In the 19th century the variational principles of mechanics that allow one to determine the extreme equilibrium (passing through the continuous sequence of equilibrium states) trajectories, as was noted in the introduction, were extended to the description of nonconservative systems (Polak, 1960), i.e., the systems in which irreversibility of the processes occurs. However, the analysis of interrelations between the notions of "equilibrium" and "reversibility," "equilibrium processes" and "reversible processes" started only during the period when the classical equilibrium thermodynamics was created by Clausius, Helmholtz, Maxwell, Boltzmann, and Gibbs. Boltzmann (1878) and Gibbs (1876, 1878, 1902) started to use the terms of equilibria to describe the processes that satisfy the entropy increase principle and follow the "time arrow."... 

Entropy in an isolated system increases dS/dt> 0 until it reaches equilibrium dS/dt = 0, and displays a direction of change leading to the thermodynamic arrow of time. The phenomenological approach favoring the retarded potential over the solution to the Maxwell field equation is called the time arrow of radiation. These two arrows of time lead to the Einstein-Ritz controversy Einstein believed that irreversibility is based on probability considerations, while Ritz believed that an initial condition and thus causality is the basis of irreversibility. Causality and probability may be two aspects of the same principle since the arrow of time has a global nature. 

Eddington underscores his high regard for the second law of thermodynamics in his view that The law that entropy always increases—the second law of thermodynamics—holds, I think, the supreme position among the laws of Nature. As an increase in entropy measures the increase in disorder, that is, the increase in randomness, Eddington developed the concept of times arrow, with the following thought ... 

As underlined by Ingegnoli (2002), scientists have to avoid two representations of nature which tend to a world of alienation (1) the deterministic one, with no possibility of novelty and creation, (2) the stochastic one, which leads to an absurd world with no causality principle and without any ability to forecast. Possibly, the major incentive toward a new conception of nature comes from scientists like W. Ashby (1962), Von Bertalanffy (1968), Weiss (1969), Lorenz (1978, 1980), Popper (1982, 1996) and Piigogine (1977, 19%), who observed how nature creates its most fine, sensitive and complex structures through non-reversible processes which are time oriented (time arrow). No doubt that thermodynamics becomes the most important physical discipline when complex adaptive systems exchanging energy, matter and information are involved with life processes. 

Eigen s theory describes the self-organisation of biological macromolecules on the basis of kinetic considerations and mathematical formulations, which are in turn based on the thermodynamics of irreversible systems. Evolutionary processes are irreversibly linked to the flow of time. Classical thermodynamics alone cannot describe them but must be extended to include irreversible processes, which take account of the arrow of time (see Sect. 9.2). Eigen s theory is based on two vital concepts ... 

These three examples (and many others that might be imagined) indicate that the first law is inadequate to provide a complete picture of the intrinsic natural time-ordering or directionality of spontaneous thermal processes. As discussed in Section 3.2 (see Table 3.1), the irreversibility of spontaneous natural events ( time s arrow ) is deeply tied to dissipative heating effects that underlie thermodynamic theory. Proper characterization of spontaneity and irreversibility in thermal processes therefore requires a further extension of the inductive basis of thermodynamic theory the second law of thermodynamics. 

A. Lasota and M.C. Mackey, Probabilistic Properties of Deterministic Systems (Cambridge University Press, Cambridge 1985) M.C. Mackey, Time s Arrow The Origins of Thermodynamic Behavior (Springer, New York 1992). 

Poets and philosophers have spoken of entropy as "time s arrow," a metaphor that arises out of the second law of thermodynamics. According to the second law, all spontaneously occurring processes are accompanied by an increase in the disorder of the universe. At some far distant time, when all is disorder and there is no order or available energy left, the universe as we know it must end. 

Notice that the direction of the process and time have been determined This has been called the arrow of time [2], Time proceeds in the direction of entropy generation, that is, toward a state of greater probability for the total of the system and its environment, which, in the widest sense, makes up the universe. Finally, we wish to point out that an interesting implication of Equation 2.10 is that for substances in the perfect crystalline state at T = 0 K, the thermodynamic probability Q = 1 and thus S = 0. 

The conclusions reached here are clearly related to those of Prigogine [160] who deduced that the irreversible creation of matter generates cosmological entropy and that the arrow of time is provided by the transformation of gravitational energy into matter. The difference is that Prigogine s result was obtained by incorporating the second law of thermodynamics into the relativistic field equations, whereas the present model makes no assumption about macroscopic behaviour. 

Catalysis relies on changes in the kinetics of chemical reactions. Thermodynamics acts as an arrow to show the way to the most stable products, but kinetics defines the relative rates of the many competitive pathways available for the reactants, and can therefore be used to make metastable products from catalytic processes in a fast and selective way. Indeed, cafalysis work by opening alternative mechanistic routes with lower activation energy barriers than those of the noncatalyzed reactions. As an example, Figure 1 illustrates how the use of metal catalysts facilitates the dissociation of molecular oxygen, and with that the oxidation of carbon monoxide. Thanks to the availability of new pathways, catalyzed reactions can be carried out at much faster rates and at lower temperatures than noncatalyzed reactions. Note, however, that a catalyst can shorten the time needed to achieve thermodynamic equihbrium, but caimot shift the position of that equihbrium, and therefore cannot catalyze a thermodynamicaUy unfavorable reaction. ... 

I have a degree in chemistry and another in physics. My first scientific publications were mostly on mixtures. In 1957, I published a book on the molecular theory of solutions. Also, my early work in thermodynamics was closer to chemistry than to physics. This has changed in the later part of my life when I became mainly involved with the microscopic roots of the arrow of time associated to entropy. This part is closer to physics. Anyway, the distinction between chemistry and physics is somewhat arbitrary. My later work is dominated by my belief that the direction of time is of fundamental importance in nature. This was the main conclusion of my studies of non-equilibrium thermodynamics. 

The 19th century left us with a conflicting heritage. Classical mechanics and even quantum mechanics and relativity are time-symmetrical theories. The past and the future play the same role in them. On the other hand, thermodynamics introduces entropy, and entropy is associated to the arrow of time. So we have two descriptions of nature. Simplifying somewhat, we may say that the first emphasizes being and the second becoming. This leads to many questions. What is the role of entropy and of distance to equilibrium in nature And a second question is, how does the time-symmetry breaking of entropy relate to the laws of physics ... 

Re Entry [63], Ref. [63]) Reference [63] considers various aspects of the Second Law of Thermodynamics and its relation to the arrow of time and to cosmology. Reference [63] was for sale at the 27th Texas Symposium on Relativistic Astrophysics, held at the Fairmont Hotel in Dallas, Texas, December 8-13, 2013. 

Elixirs of youth are perpetual motion machines of the second kind. They violate the second law of thermodynamics. Life is highly organized and requires energy to maintain this order, a machine (the fountain of youth) that can magically create order out of the normal process of the forward arrow of time must violate the second law. 

The paradox can be resolved in assuming that in cosmology there is an arrow of time. On the other hand, by fluctuations, the second law of thermodynamics may be violated [14]. 

Entropy and Arrow of Time To sum up In a thermally insulated system, entropy can increase but never decrease at best its amount remains constant. As mentioned before, this is what the second law of thermodynamics states. We can also formulate For a thermally insulated system entropy always increases for irreversible processes. It remains, however, constant for reversible processes. We can write in abbreviated form... 

The purpose here is to contrast the author s perspective of the dogged manner in which living organisms create relatively long-lived order out of chaos from the relatively more spontaneous transient creations of order arising out of the Prigogine focus on nonequilibrium thermodynamics. This brings us to consideration of the arrow of time and of evolution and natural selection. 

Murphy s law is a whimsical rule that says that anything that can go wrong will go wrong. But in an article in the Journal of Chemical Educatim, Erank Lambert writes, Murphy s law is a fraud. He also writes, The second law of thermodynamics is time s arrow, but chemical kinetics is its clock Read Lambert s article J. Chem. Ed., 74(8), 1997, p. 947), and write an essay explaining, in the context of the latter quotation, why Lambert claims that Murphy s law is a fraud. (Eor more of Professor Lambert s unique insights into thermodynamics, see his website at http //www.secondlaw.com/)... 

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