What can a better coupling between space and time concepts bring to thermodynamics?

The present text is our communication to JETC conference in Budapest (Joint European Thermodynamics conference, May 21-25, 2017). It discusses some issues referring to the relations between space, time and thermodynamics. Thermodynamics has a close relationship with time, if only for the discussion of irreversibility. But the concept of time remains mysterious and misunderstood for many, including in physics. In our view, it is absurd to consider the question of time alone: time is an abstract concept not to be separated from the world by giving it a substantial value. To understand time is to understand how one abstracts it from the movements of material entities (including photons) in space. To tell it short, time and space are of the same substance, i.e. movement: they are constructed by comparing different movements, and an arbitrary (left to free will) choice is made to define the boundary between them, depending on scale. Some consequences of this approach bear on the conceptual understanding of thermodynamics in general. The following statements, reconsidered in the new picture, are examined briefly: - there is no ultimate parting between equilibrium and non-equilibrium, heat and work, kinetics and (diffusion) transport, this is a matter of scale; - the concept of entropy, the attribution of an entropy to an individual particle, the interior and the exterior of a system and its boundary, the definition of the quantities proper to thermodynamics such as internal energy, heat etc., all derive from the understanding of the necessary link between the different scale levels at which to examine the system; - the constant association of the temporal variations and the spatial gradients (“space arrows”), of a fundamental nature, opens up to the conceptual unification of the two expressions of the second law, i.e. the phenomenological and the statistical ones. In total, it is possible to envisage a hierarchy of thermodynamics, moving from one scale level to another. We can define thermodynamics generically, or on the contrary define several, according to the variables and physical quantities defined. By getting more into the equations, avenues for research are derived from our point of view. The quantities must go in pairs of the type (f, g) like the pair (electric field, magnetic field) in electromagnetism, the pair (energy, momentum) in mechanics, the pair (concentration, flux) in thermodynamics etc., and verify laws expressing correlated variations with respect to time and space variables (within a relation-based thinking; these variations are the only thing we can know, not the single quantities themselves). For entropy S, we are invited to propose a pair (S, F), not S alone, which can be interpreted as a couple (entropy, entropy flux) or (probability of state, probability of trajectory). The previous equations are Lorentz invariant, which allows a better connection with relativity theory. The link between thermodynamics and quantum mechanics is also discussed.