In thermodynamics, irreversibility or "irreversible" is the term used by German physicist Rudolf Clausius in 1854 to describe a cyclic thermodynamic process, particularly the Carnot cycle, in which following a series of heat interactions whereby the working body yields work output and then returns to its original state, there occurs an quantifiable energy loss due to intermolecular work interactions of the atoms and molecules of the working body upon each other. [1]

Carnot | Caloric re-establishment
The following illustration shows a general outline of the jump from the 1780-1820s Lavoisier-Carnot caloric conservation model of heat and cyclical operations to the 1854 Clausius-Rankine caloric transformation equivalence-value model of heat and cyclical operations of bodies:

 (Marcet, 1805) (Carnot, 1823) (Clausius, 1854-56) $N = - \int \frac{dQ}{T} \,$ Left: a depiction of English science writer Jane Marcet's 1805 sand-marble illustrative model of capacity of a body for caloric (see: heat capacity), in which the sand represents the "caloric" and the ping pong balls represent the atoms, according to which a given body will have so much capacity for caloric, i.e. heat as it was viewed in that period. [5]Middle: French physicist Sadi Carnot's 1824 so-called re-establishment of equilibrium in the caloric, namely his model of a body being able to "reestablish" its equilibrium amount of caloric, a then considered a conserved particle, following expansion to one volume and state, followed by contraction to its original volume and state. Right: German physicist Rudolf Clausius' 1854-56 caloric conservation upgrade concept of equivalence-value of all uncompensated transformations model of irreversibility.

Overview
All natural processes are irreversible. The phenomenon of irreversibility results from the fact that if a thermodynamic system of interacting molecules is brought from one thermodynamic state to another, the configuration or arrangement of the atoms and molecules in the system will change as a result. A certain amount of "transformation energy" will be used as the molecules of the "working body" do work on each other when they change from one state to another. During this transformation, there will be a certain amount of heat energy loss or dissipation due to intermolecular friction and collisions; energy that will not be recoverable if the process is reversed.

The essence of the description and understanding of irreversibility, as defined by Clausius, is the difference between Carnot’s understanding of the production of work in a steam engine according to French chemist Antoine Lavoisier’s 1787 caloric theory and how the working body or fluid changes during each engine cycle as this contrasts with the post 1850s view of the production of work in a steam engine according to the newer kinetic theory of heat. In short, Carnot assumed that when work was produced in a steam engine, “caloric particles” would pass from a hot body (a furnace) through the steam (the “working body”) to the cold body (a river) and that following the expansion and contraction of the steam during the production of work in an engine cycle, the working body of water molecule returned, un-altered, to its original state. Clausius, however, viewed this picture differently. From this is where the concept of entropy stems.

In his 1854 memoir “On a Modified Form of the Second Fundamental Theorem in the Mechanical Theory of Heat”, in relation to the Carnot cycle, Clausius states that “it may, moreover, happen that instead of a descending transmission of heat accompanying, in the one and the same process, the ascending transmission, another permanent change may occur which has the peculiarity of not being reversible without either becoming replaced by a new permanent change of a similar kind, or producing a descending transmission of heat.” The application and understanding of Clausius' conception of irreversibility in the sphere of daily work cycles of human life is a very advanced topic in human thermodynamics, and very difficult one to pin down. [2]

Planck
In 1897, German physicist Max Planck, in his Treatise on Thermodynamics, gave the following definition of irreversibility: [4]

“That a process may be irreversible, it is not sufficient that it cannot be directly reversed. This is the case with many mechanical processes which are not irreversible. The full requirement is, that it be impossible, even with the assistance of all agents in nature, to restore everywhere the exact initial state when the process has once taken place.”

Planck, in his posthumous autobiography, summarized the term as follows: [3]

“A process which in no manner can be completely reversed I call a ‘natural’ one. The term for it in universal use today, is ‘irreversible’.”

References
1. (a) Clausius, Rudolf. (1854). "On a Modified Form of the Second Fundamental Theorem in the Mechanical Theory of Heat", (pp. 111-135).
(b) Clausius, R. (1865). The Mechanical Theory of Heat – with its Applications to the Steam Engine and to Physical Properties of Bodies. London: John van Voorst, 1 Paternoster Row. MDCCCLXVII.
2. (a) Thims, Libb. (2007). Human Chemistry (Volume One) (irreversibility, 5+ pgs). Morrisville, NC: LuLu.
(b) Thims, Libb. (2007). Human Chemistry (Volume Two) (irreversibility, 10+ pgs). Morrisville, NC: LuLu.
3. Planck, Max. (1949). Scientific Autobiography, and Other Papers (translator: Frank Gaynor) (pg. 17). Philosophical Library; Greenwood Press, 1968.
4. (a) Planck, Max. (1897). Treatise on Thermodynamics (pg. 84). New York: Dover.
(b) Hokikian, Jack. (2002). The Science of Disorder: Understanding the Complexity, Uncertainty, and Pollution in Our World (pg. 69). Los Feliz Publishing.
5. (a) Marcet, Jane. (1805). Conversations on Chemistry (pg. 66). Philadelphia: Grigg & Elliot, 1846.
(b) Jane Marcet – Wikipedia.