How Flexible Is the Concept of Local Thermodynamic Equilibrium?
It has been demonstrated by using generalized phenomenological irreversible thermodynamic theory (GPITT) that by replacing the conventional composition variables <inline-formula><math display="inline"><semantics><mrow><mo>{</mo><msub><mi>x<...
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MDPI AG
2023-01-01
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| Series: | Entropy |
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| Online Access: | https://www.mdpi.com/1099-4300/25/1/145 |
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| author | Vijay M. Tangde Anil A. Bhalekar |
| author_facet | Vijay M. Tangde Anil A. Bhalekar |
| author_sort | Vijay M. Tangde |
| collection | DOAJ |
| description | It has been demonstrated by using generalized phenomenological irreversible thermodynamic theory (GPITT) that by replacing the conventional composition variables <inline-formula><math display="inline"><semantics><mrow><mo>{</mo><msub><mi>x</mi><mi>k</mi></msub><mo>}</mo></mrow></semantics></math></inline-formula> by the quantum level composition variables <inline-formula><math display="inline"><semantics><mrow><mo>{</mo><msub><mover accent="true"><mi>x</mi><mo>˜</mo></mover><mrow><mi>k</mi><mo>,</mo><mspace width="0.166667em"></mspace><mi>j</mi></mrow></msub><mo>}</mo></mrow></semantics></math></inline-formula> corresponding to the nonequilibrium population of the quantum states, the resultant description remains well within the local thermodynamic equilibrium (LTE) domain. The next attempt is to replace the quantum level composition variables by their respective macroscopic manifestations as variables. For example, these manifestations are, say, the observance of fluorescence and phosphorescence, existence of physical fluxes, and ability to register various spectra (microwave, IR, UV-VIS, ESR, NMR, etc.). This exercise results in a framework that resembles with the thermodynamics with internal variables (TIV), which too is obtained as a framework within the LTE domain. This TIV-type framework is easily transformed to an extended irreversible thermodynamics (EIT) type framework, which uses physical fluxes as additional variables. The GPITT in EIT version is also obtained well within the LTE domain. Thus, GPITT becomes a complete version of classical irreversible thermodynamics (CIT). It is demonstrated that LTE is much more flexible than what CIT impresses upon. This conclusion is based on the realization that the spatial uniformity for each tiny pocket (cell) of a spatially non-uniform system remains intact while developing GPITT and obviously in its other versions. |
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| spelling | doaj.art-b619da4ad51041b69043e6968cd28f8d2023-11-30T22:09:19ZengMDPI AGEntropy1099-43002023-01-0125114510.3390/e25010145How Flexible Is the Concept of Local Thermodynamic Equilibrium?Vijay M. Tangde0Anil A. Bhalekar1Department of Chemistry, Rashtrasant Tukadoji Maharaj Nagpur University, Nagpur 440 033, IndiaDepartment of Chemistry, Rashtrasant Tukadoji Maharaj Nagpur University, Nagpur 440 033, IndiaIt has been demonstrated by using generalized phenomenological irreversible thermodynamic theory (GPITT) that by replacing the conventional composition variables <inline-formula><math display="inline"><semantics><mrow><mo>{</mo><msub><mi>x</mi><mi>k</mi></msub><mo>}</mo></mrow></semantics></math></inline-formula> by the quantum level composition variables <inline-formula><math display="inline"><semantics><mrow><mo>{</mo><msub><mover accent="true"><mi>x</mi><mo>˜</mo></mover><mrow><mi>k</mi><mo>,</mo><mspace width="0.166667em"></mspace><mi>j</mi></mrow></msub><mo>}</mo></mrow></semantics></math></inline-formula> corresponding to the nonequilibrium population of the quantum states, the resultant description remains well within the local thermodynamic equilibrium (LTE) domain. The next attempt is to replace the quantum level composition variables by their respective macroscopic manifestations as variables. For example, these manifestations are, say, the observance of fluorescence and phosphorescence, existence of physical fluxes, and ability to register various spectra (microwave, IR, UV-VIS, ESR, NMR, etc.). This exercise results in a framework that resembles with the thermodynamics with internal variables (TIV), which too is obtained as a framework within the LTE domain. This TIV-type framework is easily transformed to an extended irreversible thermodynamics (EIT) type framework, which uses physical fluxes as additional variables. The GPITT in EIT version is also obtained well within the LTE domain. Thus, GPITT becomes a complete version of classical irreversible thermodynamics (CIT). It is demonstrated that LTE is much more flexible than what CIT impresses upon. This conclusion is based on the realization that the spatial uniformity for each tiny pocket (cell) of a spatially non-uniform system remains intact while developing GPITT and obviously in its other versions.https://www.mdpi.com/1099-4300/25/1/145local thermodynamic equilibriumclassical irreversible thermodynamicsthermodynamic state functions in nonequilibriumGibbs relations |
| spellingShingle | Vijay M. Tangde Anil A. Bhalekar How Flexible Is the Concept of Local Thermodynamic Equilibrium? Entropy local thermodynamic equilibrium classical irreversible thermodynamics thermodynamic state functions in nonequilibrium Gibbs relations |
| title | How Flexible Is the Concept of Local Thermodynamic Equilibrium? |
| title_full | How Flexible Is the Concept of Local Thermodynamic Equilibrium? |
| title_fullStr | How Flexible Is the Concept of Local Thermodynamic Equilibrium? |
| title_full_unstemmed | How Flexible Is the Concept of Local Thermodynamic Equilibrium? |
| title_short | How Flexible Is the Concept of Local Thermodynamic Equilibrium? |
| title_sort | how flexible is the concept of local thermodynamic equilibrium |
| topic | local thermodynamic equilibrium classical irreversible thermodynamics thermodynamic state functions in nonequilibrium Gibbs relations |
| url | https://www.mdpi.com/1099-4300/25/1/145 |
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