From: <complex-science@necsi.org> (Loet Leydesdorff)
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Date: Fri, 04 Jul 2008 14:58:19 -0400
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References: <list-22003645@necsi.org>
Subject: RE: How to avoid mis-interpreting the second law of thermodynamics
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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.
> 
> 
> 
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