Dear Professor Mani: First, sincere apologies for my careless error with respect to the direction of monotonicity by not specifying the system.
I poised the question in this framework for educational purposes. Some peirce -l list serve members have extremely narrow views of the nature of Prigoginian entropy in the philosophy of science and it relation to CSP's writings. . Now, back to the points at hand, which is the relation between the term 'entropy' as it originated in the 19th Century and its role as scientific / mathematical fact with regard to heat flow and thermodynamics. Within this framework, my interest is in chemical thermodynamics as it relates to chemical symbols of the Table of Elements hence to all living organisms. Entropy is an experimental measurement of heat capacity and heat flow. Furthermore, this logic of thermodynamics is intertwined with the Law Of Mass Action for chemical equations relating to chemical change. As a mathematician / computer scientist, you are free to prune your world view to a narrower focus such that my interests are excluded . But, to the science of chemical engineering, the classical view of entropy is essential to the operations of the chemical industry, for example, petro-chamical manufacturing of fuels and plastics. Now, turning to your recommended reference to Lieb / Yngvason papers, for example, Current Developments in Mathematics, 2001, 89-129, (which is downloadable from the internet). They explicitly state that (about entropy) in the abstract and text: "This principle is independent of models, statistical mechanical or otherwise, and can be understood without recourse to to Carnot cycles, ideal gases, and other assumptions as 'heat', 'temperature', reversible processes, etc, as is usually done." Wow! Double wow! In this sentence, as I read it, Lieb / Yngvason say that the entropy principle is independent of a physical thermodynamic system! In other words, the entropy principle is independent of both physics and chemistry, yet somehow describes the behavior of physical and chemical systems. This infers that the entropy principle is merely the consequence of a particular form of mathematical function. In other words, they are saying that the a class of monotone mathematical functions can be defined that is independent of thermodynamic functions. The message is clear. To Lieb and Yngason, a mathematical principle of entropy is independent of the thermodynamic principle of entropy! Obviously, Lieb and Yngason are merely re-arranging the ordering of concepts in such a way as give a coherent mathematical interpretation of a physical concept. Mathematical concepts are moved from a consequence of nature to an antecedent of nature by invoking the concepts of "procedes" and state space. In my view, the open question is the physical generality of this re-arranging of concepts. How does one use such a conceptual re-arrangement of symbols to the predictions of chemical structures and living structures? My question to you, Professor Jani, is, do any of your 150 concepts of entropy lead to a logico-mechanical system relevant to the pan-chemical sciences? the plexus of life? With regard to your assertion: > > When we formulate logics from any physical theory, often there is > scope for variation in the abstraction. > The nature of abstraction is one of the essential topics of CSP writings. In your terminology, what is the mathematical or logical origin of your assertion that their exist a "scope of variation"? Perhaps you mean "scale"? Or, perhaps you mean "index"? Why "scope of variation"? Or, do you mean that the 150 mathematical formulations of entropy is an example of the precision of mathematical abstraction? Cheers jerry On Apr 8, 2015, at 1:15 PM, A. Mani wrote: > list, > > Jerry, > > In all contexts (coding, uncertainty, roughness), entropy is seen as a > monotonic increasing function. > > I don't like real-valued functions in rough sets, and if I need to > generalize it then would prefer a comparison based approach > > >> I am puzzled by the meaning of your statement: > >> >>> An example of abstraction of thermodynamic entropy is in the papers of >>> Elliott H. Lieb and Jakob Yngvason >> > >> Thermodynamic entropy is an abstract physical law as well as (an often >> irrelevant, for example, biological) mathematical abstraction >> about heat flow. > > > In the works of the mentioned authors, abstraction over Gibbs > thermodynamics is done. > To be specific: the Physics today paper "A Fresh Look at Entropy and the > Second Law of Thermodynamics" > > When we formulate logics from any physical theory, often there is > scope for variation in the abstraction. > > > Jon, > >> 2. >> http://inquiryintoinquiry.com/2012/12/07/triadic-relations-intentions-fuzzy-subsets-2/ >> 3. >> http://inquiryintoinquiry.com/2012/12/07/triadic-relations-intentions-fuzzy-subsets-3/ > > We need a separate thread for this. > I would be more interested in how you formulate semi-sets and type-2 fuzzy > sets. > > > > > Regards > > A. Mani > > > > Prof(Miss) A. Mani > CU, ASL, AMS, ISRS, CLC, CMS > HomePage: http://www.logicamani.in > Blog: http://logicamani.blogspot.in/ > http://about.me/logicamani > sip:[email protected] > > > On Wed, Apr 8, 2015 at 10:57 PM, Sungchul Ji <[email protected]> wrote: >> Jerry, >> >> You wrote: >> >> "An essence of thermodynamic's second law is that entropy is a monotonic >> decreasing function." >> >> I presume you meant to say "a monotonic increasing function" ? >> >> Sung >> >> On Wed, Apr 8, 2015 at 11:46 AM, Jerry LR Chandler >> <[email protected]> wrote: >>> >>> Dear Prof. Mani: >>> >>> Thank you for your informed response. >>> >>> One of the basic questions that remains open is the relation between >>> thermodynamics, entropy and life. >>> >>> The essential mathematical basis of this openness is, in my opinion, the >>> role of cycles (of any finite size.) >>> >>> An essence of thermodynamic's second law is that entropy is a monotonic >>> decreasing function. >>> >>> Given your extensive expertise in this area of copulative relations among >>> mathematic descriptions of entropies, do all of these varieties (not >>> mathematical varieties) of entropy require monotonic decreasing functions or >>> not? >>> >>> (I am aware of the fact that one can introduce periodic forcing functions >>> such that physical cycles can be introduced into thermodynamic systems. This >>> question is intended to exclude periodic forcing functions.) >>> >>> I am puzzled by the meaning of your statement: >>> >>>> >>>> An example of abstraction of thermodynamic entropy is in the papers of >>>> Elliott H. Lieb and Jakob Yngvason >>>> >>> >>> Thermodynamic entropy is an abstract physical law as well as (an often >>> irrelevant, for example, biological) mathematical abstraction about heat >>> flow. >>> >>> What is the third type of abstraction that you reference? >>> >>> BTW, I presume that you are aware of A. Ehresmann's work on the relation >>> between category theory and entropy. >>> >>> >>> Cheers >>> >>> Jerry >>> >>> >>> >>> >>> >>> On Apr 8, 2015, at 2:58 AM, A. Mani wrote: >>> >>>> Prof Jerry, list >>>> >>>> On Tue, Apr 7, 2015 at 4:44 AM, Jerry LR Chandler >>>> <[email protected]> wrote: >>>> >>>>> >>>>> My question to you is: >>>>> >>>>> Is it possible to use a crisp form of hybrid logic to separate your >>>>> meanings of entropy from thermodynamic entropy? >>>> >>>> There are over 150 types of information related entropies (many having >>>> variations of a theme flavor). >>>> >>>> In principle it should be possible to form hybrid logic or logics with >>>> correspondences if we abstract thermodynamic entropy in the >>>> statistical/mathematical way. From a practical perspective (for >>>> entropy related to rough or fuzzy sets) a correspondence result may >>>> not seen as significant because the information perspective would >>>> already be an approximate (and not exact) representation of a >>>> practical context. >>>> >>>> The results can be useful for visualization definitely. >>>> >>>> An example of abstraction of thermodynamic entropy is in the papers of >>>> Elliott H. Lieb and Jakob Yngvason >>>> >>>> >>>> From the perspective of learning, the comparison would be more >>>> significant >>>> >>>> >>>> Best >>>> >>>> A. Mani >>>> >>>> >>>> >>>> Prof(Miss) A. Mani >>>> CU, ASL, AMS, ISRS, CLC, CMS >>>> HomePage: http://www.logicamani.in >>>> Blog: http://logicamani.blogspot.in/ >>>> http://about.me/logicamani >>>> sip:[email protected] >>>> >>>> ----------------------------- >>>> PEIRCE-L subscribers: Click on "Reply List" or "Reply All" to REPLY ON >>>> PEIRCE-L to this message. PEIRCE-L posts should go to >>>> [email protected] . To UNSUBSCRIBE, send a message not to PEIRCE-L >>>> but >>>> to [email protected] with the line "UNSubscribe PEIRCE-L" in the BODY of >>>> the message. More at http://www.cspeirce.com/peirce-l/peirce-l.htm . >>>> >>>> >>>> >>>> >>> >>> >>> >>> ----------------------------- >>> PEIRCE-L subscribers: Click on "Reply List" or "Reply All" to REPLY ON >>> PEIRCE-L to this message. PEIRCE-L posts should go to >>> [email protected] . To UNSUBSCRIBE, send a message not to PEIRCE-L but >>> to [email protected] with the line "UNSubscribe PEIRCE-L" in the BODY of >>> the message. More at http://www.cspeirce.com/peirce-l/peirce-l.htm . >>> >>> >>> >>> >>> >> >> >> >> -- >> Sungchul Ji, Ph.D. >> >> Associate Professor of Pharmacology and Toxicology >> Department of Pharmacology and Toxicology >> Ernest Mario School of Pharmacy >> Rutgers University >> Piscataway, N.J. 08855 >> 732-445-4701 >> >> www.conformon.net > > ----------------------------- > PEIRCE-L subscribers: Click on "Reply List" or "Reply All" to REPLY ON > PEIRCE-L to this message. PEIRCE-L posts should go to [email protected] > . To UNSUBSCRIBE, send a message not to PEIRCE-L but to [email protected] > with the line "UNSubscribe PEIRCE-L" in the BODY of the message. More at > http://www.cspeirce.com/peirce-l/peirce-l.htm . > > > >
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