A No-Go Theorem of Analytical Mechanics for the Second Law Violation
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866912054837772288 |
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| author | Gujrati, P. D. |
| author_facet | Gujrati, P. D. |
| contents | We follow the Boltzmann-Clausius-Maxwell (BCM) proposal to solve a long-standing problem of identifying the underlying cause of the second law (SL) of spontaneous irreversibility, a stochastic universal principle, as the mechanical equilibrium (stable or unstable) principle (Mec-EQ-P) of analytical mechanics of an isolated nonequilibrium system of any size. The principle leads to nonnegative system intrinsic (SI) microwork and SI-average macrowork dW during any spontaneous process. In conjuction with the first law, Mec-EQ-P leads to a generalized second law (GSL) dQ=dW>0, where dQ=TdS is the purely stochastic SI-macroheat that corresponds to dS>0 for T>0 and dS<0 for T<0, where T is the temperature. The GSL supercedes the conventional SL formulation that is valid only for a macroscopic system for positive temperatures temperatures, but reformulates it to dS<0 for negative temperatures. It is quite surprising that GSL is not only a direct consequence of intertwined mechanical and stochastic macroquantities through the first law but also remains valid for any arbitrary irreversible process in a system of any size as an identity for positive and negative temperatures. It also becomes a no-go theorem for GSL-violation unless we abandon Mec-EQ-P of analytical mechanics used in the BCM proposal, which will be catastrophic for theoretical physics. In addition, Mec-EQ-P also provides new insights into the roles of spontaneity, nonspontaneity, negative temperatures, instability, and the significance of dS<0 due to nonspontaneity and inserting internal constraints. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_17007 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A No-Go Theorem of Analytical Mechanics for the Second Law Violation Gujrati, P. D. Statistical Mechanics Mathematical Physics Classical Physics We follow the Boltzmann-Clausius-Maxwell (BCM) proposal to solve a long-standing problem of identifying the underlying cause of the second law (SL) of spontaneous irreversibility, a stochastic universal principle, as the mechanical equilibrium (stable or unstable) principle (Mec-EQ-P) of analytical mechanics of an isolated nonequilibrium system of any size. The principle leads to nonnegative system intrinsic (SI) microwork and SI-average macrowork dW during any spontaneous process. In conjuction with the first law, Mec-EQ-P leads to a generalized second law (GSL) dQ=dW>0, where dQ=TdS is the purely stochastic SI-macroheat that corresponds to dS>0 for T>0 and dS<0 for T<0, where T is the temperature. The GSL supercedes the conventional SL formulation that is valid only for a macroscopic system for positive temperatures temperatures, but reformulates it to dS<0 for negative temperatures. It is quite surprising that GSL is not only a direct consequence of intertwined mechanical and stochastic macroquantities through the first law but also remains valid for any arbitrary irreversible process in a system of any size as an identity for positive and negative temperatures. It also becomes a no-go theorem for GSL-violation unless we abandon Mec-EQ-P of analytical mechanics used in the BCM proposal, which will be catastrophic for theoretical physics. In addition, Mec-EQ-P also provides new insights into the roles of spontaneity, nonspontaneity, negative temperatures, instability, and the significance of dS<0 due to nonspontaneity and inserting internal constraints. |
| title | A No-Go Theorem of Analytical Mechanics for the Second Law Violation |
| topic | Statistical Mechanics Mathematical Physics Classical Physics |
| url | https://arxiv.org/abs/2406.17007 |