> 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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>>
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>
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