Question: Which thermodynamic reasoning approach did the founders of thermodynamics favor?
About the article "Thermodynamics", section "States and processes".

Candidate passages:
 "For a quick reference table of these equations, see: Table of thermodynamic equations" Thermodynamics is expressed by a mathematical framework of "thermodynamic equations" which relate various thermodynamic quantities and physical properties measured in a laboratory or production process.
Thermodynamics is based on a fundamental set of postulates, that became the laws of thermodynamics. 
There are three fundamental kinds of entity in thermodynamics, states of a system, processes of a system, and thermodynamic operations.
This allows three fundamental approaches to thermodynamic reasoning, that in terms of states of thermodynamic equilibrium of a system, and that in terms of time-invariant processes of a system, and that in terms of cyclic processes of a system.
The approach through states of thermodynamic equilibrium of a system requires a full account of the state of the system as well as a notion of process from one state to another of a system, but may require only an idealized or partial account of the state of the surroundings of the system or of other systems.
The method of description in terms of states of thermodynamic equilibrium has limitations.
For example, processes in a region of turbulent flow, or in a burning gas mixture, or in a Knudsen gas may be beyond "the province of thermodynamics".
This problem can sometimes be circumvented through the method of description in terms of cyclic or of time-invariant flow processes.
This is part of the reason why the founders of thermodynamics often preferred the cyclic process description.
Approaches through processes of time-invariant flow of a system are used for some studies.
Some processes, for example Joule-Thomson expansion, are studied through steady-flow experiments, but can be accounted for by distinguishing the steady bulk flow kinetic energy from the internal energy, and thus can be regarded as within the scope of classical thermodynamics defined in terms of equilibrium states or of cyclic processes.
Other flow processes, for example thermoelectric effects, are essentially defined by the presence of differential flows or diffusion so that they cannot be adequately accounted for in terms of equilibrium states or classical cyclic processes.
The notion of a cyclic process does not require a full account of the state of the system, but does require a full account of how the process occasions transfers of matter and energy between the principal system (which is often called the "working body") and its surroundings, which must include at least two heat reservoirs at different known and fixed temperatures, one hotter than the principal system and the other colder than it, as well as a reservoir that can receive energy from the system as work and can do work on the system.
The reservoirs can alternatively be regarded as auxiliary idealized component systems, alongside the principal system.
Thus an account in terms of cyclic processes requires at least four contributory component systems.
The independent variables of this account are the amounts of energy that enter and leave the idealized auxiliary systems.
In this kind of account, the working body is often regarded as a "black box", and its own state is not specified.
In this approach, the notion of a properly numerical scale of empirical temperature is a presupposition of thermodynamics, not a notion constructed by or derived from it.
Temperature is one of the principal quantities in the study of thermodynamics. 
Non-equilibrium thermodynamics is a work in progress, not an established edifice.
This article will try to sketch some approaches to it and some concepts important for it.
Some concepts of particular importance for non-equilibrium thermodynamics include time rate of dissipation of energy (Rayleigh 1873, Onsager 1931, also), time rate of entropy production (Onsager 1931), thermodynamic fields, dissipative structure, and non-linear dynamical structure.
Of interest is the thermodynamic study of non-equilibrium steady states, in which entropy production and some flows are non-zero, but there is no time variation.
One initial approach to non-equilibrium thermodynamics is sometimes called 'classical irreversible thermodynamics'.
There are other approaches to non-equilibrium thermodynamics, for example extended irreversible thermodynamics, and generalized thermodynamics, but they are hardly touched on in the present article. 
The plain term 'thermodynamics' refers to a macroscopic description of bodies and processes.
"Any reference to atomic constitution is foreign to classical thermodynamics."
The qualified term 'statistical thermodynamics' refers to descriptions of bodies and processes in terms of the atomic constitution of matter, mainly described by sets of items all alike, so as to have equal probabilities.
Thermodynamics arose from the study of two distinct kinds of transfer of energy, as heat and as work, and the relation of those to the system's macroscopic variables of volume, pressure and temperature.
Thermodynamic equilibrium is one of the most important concepts for thermodynamics.
The temperature of a thermodynamic system is well defined, and is perhaps the most characteristic quantity of thermodynamics.
As the systems and processes of interest are taken further from thermodynamic equilibrium, their exact thermodynamical study becomes more difficult.
Relatively simple approximate calculations, however, using the variables of equilibrium thermodynamics, are of much practical value.
In many important practical cases, as in heat engines or refrigerators, the systems consist of many subsystems at different temperatures and pressures.
In practice, thermodynamic calculations deal effectively with these complicated dynamic systems provided the equilibrium thermodynamic variables are nearly enough well-defined.
Central to thermodynamic analysis are the definitions of the system, which is of interest, and of its surroundings.
The surroundings of a thermodynamic system consist of physical devices and of other thermodynamic systems that can interact with it.
An example of a thermodynamic surrounding is a heat bath, which is held at a prescribed temperature, regardless of how much heat might be drawn from it.
There are three fundamental kinds of physical entities in thermodynamics, states of a system, thermodynamic processes of a system, and thermodynamic operations.
This allows two fundamental approaches to thermodynamic reasoning, that in terms of states of a system, and that in terms of cyclic processes of a system.
A thermodynamic system can be defined in terms of its states.
In this way, a thermodynamic system is a macroscopic physical object, explicitly specified in terms of macroscopic physical and chemical variables that describe its macroscopic properties.
The macroscopic state variables of thermodynamics have been recognized in the course of empirical work in physics and chemistry.
A thermodynamic operation is an artificial physical manipulation that changes the definition of a system or its surroundings.
Usually it is a change of the permeability or some other feature of a wall of the system, that allows energy (as heat or work) or matter (mass) to be exchanged with the environment.
For example, the partition between two thermodynamic systems can be removed so as to produce a single system.
A thermodynamic operation usually leads to a thermodynamic process of transfer of mass or energy that changes the state of the system, and the transfer occurs in natural accord with the laws of thermodynamics.
Thermodynamic operations are not the only initiators of thermodynamic processes.
Also of course changes in the intensive or extensive variables of the surroundings can initiate thermodynamic processes.
A thermodynamic system can also be defined in terms of the cyclic processes that it can undergo.
A cyclic process is a cyclic sequence of thermodynamic operations and processes that can be repeated indefinitely often without changing the final state of the system.
For thermodynamics and statistical thermodynamics to apply to a system subjected to a process, it is necessary that the atomic mechanisms of the process fall into one of two classes: those so rapid that, in the time frame of the process of interest, the atomic states effectively visit all of their accessible range, bringing the system to its state of internal thermodynamic equilibrium; and those so slow that their progress can be neglected in the time frame of the process of interest.
The rapid atomic mechanisms represent the internal energy of the system.
They mediate the macroscopic changes that are of interest for thermodynamics and statistical thermodynamics, because they quickly bring the system near enough to thermodynamic equilibrium.
"When intermediate rates are present, thermodynamics and statistical mechanics cannot be applied."
Such intermediate rate atomic processes do not bring the system near enough to thermodynamic equilibrium in the time frame of the macroscopic process of interest.
This separation of time scales of atomic processes is a theme that recurs throughout the subject.
For example, classical thermodynamics is characterized by its study of materials that have equations of state or characteristic equations.
They express equilibrium relations between macroscopic mechanical variables and temperature and internal energy.
They express the constitutive peculiarities of the material of the system.
A classical material can usually be described by a function that makes pressure dependent on volume and temperature, the resulting pressure being established much more rapidly than any imposed change of volume or temperature.
The present article takes a gradual approach to the subject, starting with a focus on cyclic processes and thermodynamic equilibrium, and then gradually beginning to further consider non-equilibrium systems.
Thermodynamic facts can often be explained by viewing macroscopic objects as assemblies of very many microscopic or atomic objects that obey Hamiltonian dynamics.
The microscopic or atomic objects exist in species, the objects of each species being all alike.
Because of this likeness, statistical methods can be used to account for the macroscopic properties of the thermodynamic system in terms of the properties of the microscopic species.
Such explanation is called statistical thermodynamics; also often it is referred to by the term 'statistical mechanics', though this term can have a wider meaning, referring to 'microscopic objects', such as economic quantities, that do not obey Hamiltonian dynamics.