A No-Go Theorem of Analytical Mechanics for the Second Law Violation

TL;DR

This paper presents a no-go theorem showing that the generalized second law of thermodynamics, derived from analytical mechanics principles, cannot be violated without abandoning fundamental mechanics, impacting our understanding of irreversibility and negative temperatures.

Contribution

It introduces a no-go theorem demonstrating the impossibility of violating the generalized second law within the analytical mechanics framework, even for negative temperatures.

Findings

The GSL is a consequence of mechanical and stochastic macroquantities.

The GSL remains valid for systems of any size and temperature.

Violating the GSL would require abandoning the Mec-EQ-P principle, which is fundamental.

Abstract

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.