Model of a thermodynamic system acting as a "refrigerator", which performs the reverse effect of a heat engine, by removing heat from a low temperature region or source (say the volume of the region inside of a freezer), by contact with a working substance (shown as the circle, above), being typically a gas, such as ammonia or carbon dioxide, which is forced to compression by an external energy or work input (say from the power company, i.e. a separate heat engine), and then passing this removed heat to a third body, i.e. the heat sink or body of air surrounding the refrigerator in the kitchen. [7] The "heat source", shown here, at a temperature of TL, or T1 in Ubbelohde's notation, is the region of local entropy decrease or "life" as Ubbelohde would see things.
In life thermodynamics, local entropy decrease is a postulate that living organisms represent an increase in order and thus effect a local decrease in entropy, a term assumed to be equivalent to disorder, in the context of the universe; and it is argued that this decrease in local entropy runs on either a greater increase in entropy in the surroundings or on energy from the sun. [1]

Overview
In 1933, James Jeans, in his The New Background of Science, was speaking of "local exceptions" to the general law of entropy increase.

Ubbelohde
In 1947, Belgian-born English thermodynamicist Alfred Ubbelohde, in his Time and Thermodynamics, gave a derivation that the chilled space inside of a refrigerator is a region of "local decrease in entropy" and then extends this idea to life in his later section “Experimental Aspects of the Relation between Thermodynamics and Life”.

To make this argument, Ubbelohde states that in the ordinary domestic refrigerator an engine pumps heat from the chilled space to the warmer kitchen air. Thus for Q1 units of heat abstracted from the chilled space at temperature T1 this chilled region is losing: [3]

$\frac{Q_1}{T_1} \,$

units of entropy. But, he qualifies, this can only happen by means of a motor. If W units of work have to be supplied by the motor, in order to abstract Q1 units of heat from the chilled space, the heat given up to the kitchen air at a temperature T2 will be:

$Q_2 = Q_1 + W \,$

and the entropy increase in the kitchen air will be:

$\frac{Q_2}{T_2} = \frac{Q_1 + W}{T_2} \,$

He then states that the resultant effect of all the various changes linked together results in a net entropy increase in the system considered as a whole. He concludes:

“Nothing forbids local entropy decrease, but these must be paid for by somewhat greater increases of entropy within the same system (often in the immediate neighborhood).”

This seems to be the root of the quote that people ever-since have been using to explain the existence of life. Although not directly stated, this concludes or alludes to the idea that life is like an ordered ice cube. In any event, Ubbelohde concludes with the statement that “the possibility of carrying out processes in local regions with decreasing entropy is important for understanding the relationship between thermodynamics and life”.

Bertalanffy
In 1950, Ludwig Bertalanffy, in his “The Theory of Open Systems in Physics and Biology”, citing Ilya Prigogine (1946) and Erwin Schrodinger (1943), stated the following: [8]

“Living systems—as open systems—maintain themselves in a steady state by the importation of materials rich in free energy, can avoid the increase of entropy which cannot be averted in closed system.”

In 1956, Judson Herrick was paraphrasing Bertalanffy as follows: [9]

“The living mechanism is an ‘open system’ (Bertalanffy, 1950), with constant interchange of materials and energy with the environment. In the living body there is a local arrest or reversal of entropy, with increase of heterogeneity and complexity rather than trend toward degradation to homogeneous low-level organization.”

Here, to note, “local” and “reversal” are Herrick’s own terms, as Bertalanffy does not use these specific terms.

Difficulties on theory
The difficulties in this assertion, aside from the obvious fact that cooling a chemical system will not bring about what is considered to be life, but rather the converse situation seems to be the case, as typified by Darwin’s warm pond model, i.e. that one has to heat a system of chemicals to bring about the synthesis of ordered intelligent animate matter, is that in earth-confined systems, which are isothermal-isobaric systems on average, it is free energy decrease, and thus process or system “entropy increase”, which actually favors evolution and thus the creation or ordered animate matter, rather than entropy decrease, as Ubbelohde postulates.

Life
Later, Ubbelohde goes on to argue that living organisms have a “disentropic behavior” or a behavior opposite to that of entropy. In more detail, building on the hypothesis of Scottish physicist James Maxell’s 1867 thermodynamic “demon”, where it is argued that to evade the second law the demon, at the doorway to a two-compartment system of gas molecules, one hot, one cold, would have to “select” all the faster moving molecules from the mixture to effect a cold to hot heat transfer, Ubbelohde states that:

“If Maxwell’s idea of selection applies in some form to living organisms, we might expect their behavior to be completely disentropic, and within a closed system containing living organisms there might be a net decrease in entropy, in the course of time.”

In contrast to this proposal, Ubbelohde outlines a second proposal, which he favors:

“Living organisms are characterized thermodynamically not by any vital power of selection of individual molecules, but by the fact that the organism considered as a unit is continually effecting processes, in which the entropy decreases, at the expense of rather greater compensating increases of entropy in the surroundings.”

Moreover, he states that living beings are “parasites on the entropy fund of the universe.” On this basis, he states:

“Living things would be so organized to effect local entropy decreases continually, so as to direct molecular processes to specific ends; this activity would, however, depend on appropriate food supplies, since it would be the conversion of food-stuffs into waste matter with higher entropy content that would compensate for the entropy decrease associated with specific behavior, and that would, on balance, give a net increase of entropy.”

In conclusion, Ubbelohde notes that further experimental tests will be needed to determine which of the two scenarios, i.e. Maxwell’s selection method (organisms being absolutely disentropic and swim upstream in the main current of entropy) or the local entropy decrease method (organisms being regions of local entropy decrease moving upstream by skilful use of local eddies within the current), is to be the explanation of the behavior of living organisms.

Other views
In 1950, American biologist Harold Blum stated: [6]

“Since any increase in order within the biosphere must be very small compared to the increase of entropy in the sun-earth system there is no reason to think that evolution controverts the second law of thermodynamics … local parts of the system may for a time increase in order.”

In 1950, American mathematican Norbert Wierner stated a near-similar version: [5]

Life … represent[s] pockets of decreasing entropy in a framework in which the large entropy tends to increase.”

In 1963, American physicist Robert Lindsay parlayed the concept of “local” entropy effects into a theory of local “entropy consumption”. In particular, Lindsay states: [3]

Local consumption of entropy is not to be considered a genuine violation of the second law, for it seems altogether likely that the entropy consumption of living things is compensated for by the corresponding entropy production elsewhere in the universe.”

In another 1964 sense, professed by English scientist James Lovelock, during the time when NASA had begun to make plans to look for life on Mars, a “reversal” or “reduction” in entropy was postulated to represent a sign of life in the universe; supposing, for instance, one were to build life detection equipment to look for life on other planets. [4]

Summary
In sum, what seems to be the case is that the concept of: "local decreased in entropy = life", is kind of a dumbed-down version of the loose idea that entropy increase equates to disorder increase, which is not necessarily the case, combined with the loose idea that life or evolution equates to order increase, thus, combined, local entropy decrease is conceived as being a universal synonym for "local order increase".

In origins, this seems to be an entropology-like argument culled from a crude extrapolation of Maxwell's demon logic, the idea of material entropy, and a mix of the disorder views of entropy professed by Austrian physicist Ludwig Boltzman in his gas theory. In this view, the term does not seem to be a rigorous one, in the chemical thermodynamics sense of a person being a "human molecule", and may in fact be non-logical. In a more logical sense, the entropic relations involved in surface thermodynamics would be a more logical branch of thermodynamics to cull from over that of statistical thermodynamics of gas-phase particles.

See also
Entropy reduction
Second law (disordering) evolution (ordering) reconciliations

References
1. Tobin, Allan J. and Dusheck, Jennie. (2004). Asking About Life, (pg. 516). Brooks Cole.
2. Ubbelohde, Alfred René. (1947). Time and Thermodynamics, (section “Experimental Aspects of the Relation between Thermodynamics and Life”, pgs. 100-05). Oxford University Press.
3. Lindsay, Robert B. (1963). The Role of Science in Civilization, (section: "Information Theory and Thermodynamics: Entropy", pgs. 153-65; section: "A Scientific Analogy: The Thermodynamic Imperative", pgs. 290-98). Westport: Greenwood Press. Dowden, Hutchinson & Ross.
4. Lovelock, James. (1979). Gaia - a New Look at Life on Earth. Oxford: Oxford University Press.
5. Wiener, Norbert. (1950). The Human Use of Human Beings; Cybernetics and Society, (pg. 32). Boston: Houghton Mifflin Co.
6. Blum, Harold F. (1951). Time's Arrow and Evolution. Princeton: Princeton University Press.
7. Dincer, Ibrahim and Kanoglu, Mehmet. (2010). Refrigeration Systems and Applications (pgs. 107). Wiley.
8. Bertalanffy, Ludwig. (1950). “The Theory of Open Systems in Physics and Biology” (pdf), Science, 111:23-29.
9. (a) Bertalanffy, Ludwig. (1950). “The Theory of Open Systems in Physics and Biology” (pdf), Science, 111:23-29.
(b) Herrick, Charles J. (1956). The Evolution of Human Nature (abs) (pg. 46). University of Texas Press.