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:girlprofes...@ekiga.net On Wed, Apr 8, 2015 at 10:57 PM, Sungchul Ji <s...@rci.rutgers.edu> 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 > <jerry_lr_chand...@me.com> 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 >> > <jerry_lr_chand...@me.com> 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:girlprofes...@ekiga.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 >> > peirce-L@list.iupui.edu . To UNSUBSCRIBE, send a message not to PEIRCE-L >> > but >> > to l...@list.iupui.edu 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 >> peirce-L@list.iupui.edu . To UNSUBSCRIBE, send a message not to PEIRCE-L but >> to l...@list.iupui.edu 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
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