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Mailing List complex-science@necsi.org Message #9638 | |
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| Very clear! Best wishes, Loet > -----Original Message----- > From: complex-science@necsi.org [mailto:complex-science@necsi.org] > Sent: Tuesday, July 01, 2008 5:47 AM > To: complex-science@necsi.org > Subject: How to avoid mis-interpreting the second law of > thermodynamics > > The most general way to express the second law of thermodynamics is in > terms of the following formalism introduced by Prigogine > (1917-2003) in > 1967 [1]: > > dS = d_eS + d_iS . . . . . . . . . . . . . . > . . . . . . (1) > > where dS is the overall entropy change experienced by the system under > consideration, d_eS (i.e., "d subscript e S")is the entropy exchanged > between the system and its environment, and d_iS is the > entropy change due > to irreversible processes occurring within the system such as > diffusion > and chemical reactions. > > Using Eq. (1), we can express the second law as follows [1]: > > "Whenever irreversible processes occur within a system, > d_iS > 0." . . (2) > > Statement (2), when applied to isolated and non-isolated > (which includes > both closed and open) systems, leads to the following corollaries: > > "The entropy of isolated systems increases with time." . > . . . . . . (3) > > "The entropy of non-isolated system can increase, > decrease or remain constant with time." . . . . > .. . . . . (4) > > Statement (3) was first articulated by Rudolf Clausius > (1822-1888) around > 1867 [1] and is the familiar form in which the second law is usually > presented in text books, and Statement (4), alhtough obvious from the > non-equilibrium thermodyanics point of view and most relevant > to biology, > is unfortunately less well-known among biologists. > > For convenience, these statements of the second law are > re-iterated in a > tabular form in Table 1, where the third column represents > Statement (2), > the second row and the last column represents Statement (3), > and the third > row and the last column represents Statement (4). > > > Table 1. Different meanings of the second law depending > on whether the > thermodynamic system under consideration is isolated or non-isolated. > ____________________________________________________________________ > > System d_eS d_iS dS > ____________________________________________________________________ > > Isolated 0 > 0 > 0 > ____________________________________________________________________ > > Non-isolated > (i.e, closed >, < or = 0 > 0 >, < or = 0 > or open) > ____________________________________________________________________ > > > One common error found in biological literature seems to arise from > conflating d_iS and dS, leading to the erroneous conclusion that the > entropy of the system under consideration increases with time > regardless > of whether or not the system is isolated. The consequence of this > seemingly minor error in reasoning can be serious and far-reaching in > biological discourses. > > With all the best. > > Sung > > ___________________________________________ > Sungchul Ji, Ph.D. > Department of Pharmacology and Toxicology > Rutgers Unviersity > Piscataway, N.J. 08855 > > > > Reference: > [1] Kondepudi, D. and Prigogine, I. (1998). Modern > Thermodynamics: From > Heat Engines to Dissipative Structures. John Wiley & Sons, > Chichester. > P. 88. > > > > -------------------------------------------------- > For information about this discussion group visit > http://necsi.org/discuss/discuss.html > |
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