|American physicist Stephen Hawking's 1996 depiction of the thermodynamic arrow, in relation to the other arrows of time. |
In 1908, there was a debate between Swiss physicist Walter Ritz and German-born American physicist Albert Einstein as to which arrow, the electromagnetic or the thermodynamic, reduces to the other. 
In 1928,English astronomer Arthur Eddington introduced term “thermodynamic arrow” is a synonym for the 1928 term "time's arrow".
The phrase thermodynamic arrow, however, is often used in comparison to other arrows of time (numbering up to seven), such as the cosmological arrow, referring to the expansion, contraction, or movement of the universe, the psychological arrow, the sense of the movement of time according to the human psyche, or the electromagnetic arrow, the measure of time according to the movement of radiation.
In 1973 commentary on the suggestion that thermodynamic irreversibility is due to cosmological expansion, i.e. that the thermodynamic arrow is a resultant effect of the cosmological arrow, English thermodynamicist Peter Landsberg stated that “in a sense cosmology contains all subjects because it is the story of everything, including biology, psychology and human history … in that sense it can be said to contain an explanation also of time’s arrow. But this is not what is meant by those who advocate the cosmological explanation of irreversibility. They imply that in some way the time arrow of cosmology imposes its sense on the thermodynamic arrow. I wish to disagree with this view.” 
In 1988, British physicist Stephen Hawking, in his A Brief History of Time, argued that the psychological arrow, described by him as “the direction in which we feel time passes”, is determined by the thermodynamic arrow, which he likens to “the direction of time in which disorder or entropy increases”, and that these two arrows point in the same direction. 
1. (a) Ritz, Walter and Einstein, Albert. (1909). Zum gegenwärtigen Stand des Strahlungsproblems
(On the Current State of the Radiation Problem). Physikalische Zeitschrift, 10, 323-324.
(b) Fritzius, Robert S. (2006). “The Ritz-Einstein Agreement to Disagree”, Online work.
2. Landsberg, Peter T. (1973). “Thermodynamics, Cosmology, and the Physical Constants”, in J. T. Fraser (ed.), The Study of Time III (1973), pgs. 117-8.
3. Hawking, Stephen. (1996). The Illustrated - A Brief History of Time, (ch. 9: "The Arrow of Time", pgs. 182-95). New York: Bantam Books.