Question: The founders of thermodynamics preferred which approach to thermodynamic reasoning?
About the article "Thermodynamics", section "States and processes".

Candidate passages:
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. 
Advanced thermodynamics provides the relation formula_155.
From this, further mathematical and thermodynamic reasoning leads to another relation between classical calorimetric quantities.
The difference of specific heats is given by formula_156.  
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. 
 "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.