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We present an overview of the modern approaches to continuum nonequilibrium thermodynamics from the perspective of their connection with the problem of heat conduction with finite speed. The celebrated Cattaneo and Guyer–Krumhansl equations for the evolution of the heat flux are reinspected in the framework of the different thermodynamic theories which, in such a way, are reviewed and compared.

On the basis of linear non-equilibrium thermodynamic theory, exergy transfer analyses of laminar and turbulent forced convection are conducted in terms of external flows over a flat plate. Two kinds of non-dimensional concepts involving the definition of the local and mean exergy transfer Nusselt number and non-dimensional exergy flux are incorporated into exergy transfer analysis. The new analytical expressions for the local and mean exergy transfer Nusselt number and non-dimensional exergy flux are adopted to describe the exergy transfer characteristics over a flat plate. By taking air as working fluid, the influences of flat plate geometry, Reynolds number, and other operating parameters on the exergy transfer Nusselt number and non-dimensional exergy flux are examined. It is shown how the flow geometric parameters and Reynolds number, etc., may be selected in order to maximize the exergy utilization associated with a specific external convection process. In addition, the results obtained from exergy transfer analysis are compared with those obtained from traditional heat transfer analysis.

Diffusion and permeation are discussed within the context of irreversible thermodynamics. A new expression for the generalized Stokes–Einstein equation is obtained which links the permeability to the diffusivity of a two-component solution and contains the poroelastic Biot–Willis coefficient. The theory is illustrated by predicting the concentration and pressure profiles during the filtration of a protein solution. At low concentrations the proteins diffuse independently while at higher concentrations they form a nearly rigid porous glass through which the fluid permeates. The theoretically determined pressure drop is nonlinear in the diffusion regime and linear in the permeation regime, in quantitative agreement with experimental measurements.

In recent times whole-genome gene expression analysis has turned out to be a highly important tool to study the coordinated function of a very large number of genes within their corresponding cellular environment, especially in relation to phenotypic diversity and disease. A wide variety of methods of quantitative analysis has been developed to cope with high throughput data sets generated by gene expression profiling experiments. Due to the complexity associated with transcriptomics , especially in the case of gene regulation phenomena, most of these methods are of a probabilistic or statistical nature. Even if these methods have reached a central status in the development of an integrative, systematic understanding of the associated biological processes, they very rarely constitute a concrete guide to the actual physicochemical mechanisms behind biological function, and the role of these methods is more on a hypotheses generating line. An important improvement could lie in the development of a thermodynamic theory for gene expression and transcriptional regulation that will build the foundations for a proper integration of the vast amount of molecular biophysical data and could lead, in the future, to a systemic view of genetic transcription and regulation.