The paper contains a systematic exposition of a statistical method which leads to a characterization of relevant equilibrium and stability properties of the collisionless Vlasov (collective) plasma configurations according to a formalism similar to that of classical thermodynamics of the Maxwellian systems. We retake ex novo a statistical model, proposed in earlier works, in which the basic objects of the statistics are volume elements in a configurational space of the charge or of the current density. The probability distribution in this space is calculated subject to a constraint which expresses the existence of static equilibria involving only the smeared out or collective part of the densities above, while the collective energy is uncorrelated to the fluctuations arising from the single particle structure. It is one of the aims of the present paper to show that the thermodynamic quantities arising automatically in the formalism, as for instance the entropy, can be consistently inserted in the physical and conceptual context of classical thermodynamics. This is achieved by studying in detail a reversible energy interaction between the collective system and the external world, so as to identify the entropy variations calculated with the model, to those of the entropy conventionally defined. Our thermodynamic concepts will be illustrated by applications to electrostatic Vlasov equilibria (in unstable situations and in the Maxwellian limit) and to magnetic systems, both in a case open to the energy interaction with the external world (the tokamak) or in the case of an isolated system (a plasma enclosed in a perfectly conductive shell).