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In thermodynamics, the heat $Q$ is defined as a type of energy in transfer, and is not a state function, which function denotes the energy of thermal motion within a system? …

Statistical mechanics is restricted to the postulate of the equal a priori probability, but this postulate does not need to be considered for thermodynamics, so the valid ranges of statistical mechanics … and the second law of thermodynamics are different. …

There is a new statement on the second law: "irreversibility root in a fundamental principle: the gradients of the four thermodynamic forces spontaneously tend to zero". Please see http://arxiv.org/a …

If we want to obtain the mathematical proof of the second law from thermodynamics, we must consider the mathematical proof of the entropy first, as a state function. … The valid range of H-theorem is less than the second law of thermodynamics. There are some computer simulations for H theorem, the changes in H are not monotonous. …

This is a good question, but the answer is that the energy equations of thermodynamics and dynamics now cannot correspond to one by one, completely, in that the theoretical structures of the two theories …

According to the first law of thermodynamics \begin{align}U=TS+YX+\sum_j\mu_jN_j.\end{align} Where $Y$ is the generalized force, $dX$ is the generalized displacement. …

On the other hand, the postulate of the equal a priori probability does not need to be considered for thermodynamics, please consider local non-equilibrium thermodynamics, in the equation \begin{align … Time-symmetric laws of dynamics should compare with the first law of thermodynamics but not the second law. How do you prove the second law of thermodynamics from statistical mechanics? …

There has been a new approach that you may consider. Your question involves the energy conversion between heat energy and Gibbs free energy. Since the two both are non- conserved quantities, the chang …

The two scenarios you mentioned both are correct, “the pressure $p$ has different sign from other generalized force, if we increase the pressure, the volume increases, whereas if we increase the force …

The fundamental equation of thermodynamics \begin{align}\mathrm dS=\frac{\mathrm dU}{T}-\frac{Y~\mathrm dx}{T}-\sum_j\frac{\mu_j~\mathrm dN_j}{T}+\frac{p~\mathrm dV}{T}. … \end{align} Question: 1) $\Omega$ depend on the postulate of the equal a priori probability, but this postulate does not need to be considered in thermodynamics. …

\end{align} From non-equilibrium thermodynamics, we have \begin{align} dS =d_eS+d_iS.\end{align} Where $d_eS $ denotes the entropy flux, and $d_iS $ denotes the entropy production. … \end{align} In thermodynamics, we have defined the heat in transfer $Q$, but failed to take into account a function to describe the energy of thermal motion within the system. …

This topic makes some sense, “Thermodynamics quantities like pressure, temperature and entropy are associated with overall states of a macroscopic system” or associated with overall states of a local, … So thermodynamics now is a “Grey box theory”. In some new theoretical models[1], the Intensive variables $T, p$ can be instead, by the distribution of the extensive variables associated with them. …