dorsal/arxiv
View SchemaThermodynamic derivation of reciprocal relations
| Authors | Elias P. Gyftopoulos |
|---|---|
| Categories | |
| ArXiv ID | physics/0406004 |
| URL | https://arxiv.org/abs/physics/0406004 |
Abstract
Reciprocal relations correlate fairly accurately a great variety of experimental results. Nevertheless, the concepts of statistical fluctuations, and microscopic reversibility - the bases of the accepted proof of the relations by Onsager - are illusory and faulty, and contradict the foundations of the science of thermodynamics. The definitions, postulates, and main theorems of thermodynamics are briefly presented. It is shown beyond a shadow of a doubt that thermodynamics is a nonstatistical science that applies to all systems (both macroscopic, and microscopic, including systems that consist either of only one structureless particle, or only one spin), to all states (both thermodynamic or stable equilibrium, and not stable equilibrium), and that includes entropy as a well defined, intrinsic, nonstatistical property of any system in any state, at any instant in time. In the light of this novel conception of thermodynamics, we find that reciprocal relations result from a well known mathematical theorem, to wit, given a well behaved analytic function of many variables then the second derivative of the function with respect to any two variables is independent of the order of differentiation, namely, whether the first derivative is taken with respect to the one or the other of the two variables.
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"abstract": "Reciprocal relations correlate fairly accurately a great variety of\nexperimental results. Nevertheless, the concepts of statistical fluctuations,\nand microscopic reversibility - the bases of the accepted proof of the\nrelations by Onsager - are illusory and faulty, and contradict the foundations\nof the science of thermodynamics. The definitions, postulates, and main\ntheorems of thermodynamics are briefly presented. It is shown beyond a shadow\nof a doubt that thermodynamics is a nonstatistical science that applies to all\nsystems (both macroscopic, and microscopic, including systems that consist\neither of only one structureless particle, or only one spin), to all states\n(both thermodynamic or stable equilibrium, and not stable equilibrium), and\nthat includes entropy as a well defined, intrinsic, nonstatistical property of\nany system in any state, at any instant in time. In the light of this novel\nconception of thermodynamics, we find that reciprocal relations result from a\nwell known mathematical theorem, to wit, given a well behaved analytic function\nof many variables then the second derivative of the function with respect to\nany two variables is independent of the order of differentiation, namely,\nwhether the first derivative is taken with respect to the one or the other of\nthe two variables.",
"arxiv_id": "physics/0406004",
"authors": [
"Elias P. Gyftopoulos"
],
"categories": [
"physics.chem-ph"
],
"title": "Thermodynamic derivation of reciprocal relations",
"url": "https://arxiv.org/abs/physics/0406004"
},
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