Extension Opérationnelle de l’Approche de Carnot-Clausius à des Entropies de Non Equilibres et Seconde loi de la Thermodynamique pour des Températures Positives et Négatives

The review introduces a recently developed generalized nonequilibrium (NEQ) statistical thermodynamics, called Gen-Th and Gen-GSL-Th, having a mechanical foundation in which stochasticity is introduced but not the second law (SL) by following the Boltzmann-(Carnot-Clausius)-Gibbs-Maxwell (BCGM) proposal. Gen-Th is applicable to any system of any size in any arbitrary state, isolated or not, requires new techniques, clarifies various confusing points such as about generalized and exchange macroworks, and yielding many new results. Distinction between uniform and nonuniform deterministic Hamiltonians and their microstates, operationally defined internal variables and NEQ entropy S in an extended state space, and their temporal evolution are the new tools to formulate Gen-Th. By imposing mechanical equilibrium (stable or unstable) principle (Mec-EQ-P) of analytical mechanics, we formulate a generalized second law (GSL), whose form (but not of SL) remains invariant for both positive and negative temperatures T . The entropy S provides an extension of the Carnot-Clausius approach to equilibrium (EQ) entropy. We clarify the concept of spontaneous processes for both positive and negative NEQ temperatures so that dS ≥ 0 forT >0 and dS < 0 forT < 0 without violating GSL/SL. We prove a no-go theorem for the impossibility of a violation of GSL/SL for spontaneous processes. Any violation of GSL/SL is due to nonspontaneous processes such as a creation of internal constraints that are not covered by GSL/SL. Some examples are given including metastable macrostates during vitrification for positive T . We end with some open problems, some of which are also relevant for glasses.

The review introduces a recently developed generalized nonequilibrium (NEQ) statistical thermodynamics, called Gen-Th and Gen-GSL-Th, having a mechanical foundation in which stochasticity is introduced but not the second law (SL) by following the Boltzmann-(Carnot-Clausius)-Gibbs-Maxwell (BCGM) proposal. Gen-Th is applicable to any system of any size in any arbitrary state, isolated or not, requires new techniques, clarifies various confusing points such as about generalized and exchange macroworks, and yielding many new results. Distinction between uniform and nonuniform deterministic Hamiltonians and their microstates, operationally defined internal variables and NEQ entropy S in an extended state space, and their temporal evolution are the new tools to formulate Gen-Th. By imposing mechanical equilibrium (stable or unstable) principle (Mec-EQ-P) of analytical mechanics, we formulate a generalized second law (GSL), whose form (but not of SL) remains invariant for both positive and negative temperatures T . The entropy S provides an extension of the Carnot-Clausius approach to equilibrium (EQ) entropy. We clarify the concept of spontaneous processes for both positive and negative NEQ temperatures so that dS ≥ 0 forT >0 and dS < 0 forT < 0 without violating GSL/SL. We prove a no-go theorem for the impossibility of a violation of GSL/SL for spontaneous processes. Any violation of GSL/SL is due to nonspontaneous processes such as a creation of internal constraints that are not covered by GSL/SL. Some examples are given including metastable macrostates during vitrification for positive T . We end with some open problems, some of which are also relevant for glasses.

Uniform Hamiltonian Nonuniform Hamiltonian Mechanical Equilibrium Principle Irreversibility Dissipation n Carnot-Clausius Entropy Positive and Negative Temperatures

Uniform Hamiltonian Nonuniform Hamiltonian Mechanical Equilibrium Principle Irreversibility Dissipation n Carnot-Clausius Entropy Positive and Negative Temperatures