justice (labeled)
A depiction of some of the main issues at hand in regards to the concept of justice, namely: belief in the concept of free will amid an atomic-force based, or fermion-boson structured deterministic universe, internal force coupled to external force mechanisms of the mind, social balance and or imbalance, retribution, legislature, the morality of an existive justice system, righting wrongdoings, etc.
In terminology, justice (TR:94) refers to the principles or ideas related to right, as opposed to wrong, action or judgment.

Determinism | Free will
In circa 300BC, Greek natural philosopher Zeno of Citium outlined the basics of punishment and justice in a deterministic universe via his famous slave stealing parable.

In 1978, in the case of United States v. Grayson, the Supreme Court gave its legislative stance on “free will”, arguing that belief in free will is a "universal and persistent" foundation of the system of law, distinct from "a deterministic view of human conduct that is inconsistent with the underlying precepts of the criminal justice system." A repercussion of this ruling, is that any scientific developments that threaten our notion of free will would seem to put the ethics of punishing people for their bad behavior in question." [4]

Thermodynamics
In 1983, Michael Feeley, in his Court Reform on Trial, pointed out how a major change in one part of a justice system, may affect decisions in other parts, or in his own words set off a “chain reaction throughout the entire system”, thus forcing officials to adapt, which thus sometimes creates new and unanticipated problems. [7]

In 1994, American criminal justice historian Samuel Walker (Ѻ)(Ѻ), citing evidence, e.g. that California’s three strikes law is rarely used, as well as the finding that the use of the death penalty is so rare that it is comparable to be being struck by lightning, mixed Feeley’s chain reaction premise together with Newton’s third law of motion to argue that in the court system, “actions produce reactions”, and that this actuates in the form of what he refers to as a “law of criminal justice thermodynamics”, which he formulates as follows: [8]

“A major increase in the severity of the penalty will result in less frequent application of that penalty.”

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Other
Scottish social philosopher Adam Smith’s formulation of justice, supposedly, is a negative formulation of Vilfredo Pareto's optimality. (Ѻ)

Danish physicist Niels Bohr, according to Bruce Lindsay (1983), somewhere applied his complementarity principle of quantum mechanics to domain of human experiences, the complementary aspects of love and justice, specifically. [3]

Recently, American Curtis Blakely, a criminal justice professor, has been working on sociophysics of inmate population dynamics.

Justice (labeled)
A justice goddess killing an older justice goddess depiction. (Ѻ)
Quotes
The following are related quotes:

“Justice is doing what should be, injustice is not doing what should be, but turning aside from it.”
— Democritus (c.420BC) Fragment D120; cited by Stobaeus (c.550BC) in Ethics (IV.2.14) [10]

“Since justice too was introduced according to the relationship of men to each other and to the gods, if there are no gods, justice too will not exist. And this is absurd. So the followers of Pythagoras and Empedocles and the rest of the Italian group say that we have a kind of communion not only with each other and the gods but also with irrational animals. For there is one spirit penetrating the entire cosmos, like a soul, which also unites us with them.”
— Sextus Empiricus (c.200 ACM), Against the Mathematicians (9.126-130) [9]

“Power, truth, justice: they are words that denote something great, but that something we are quite unable to see and conceive.”
— Michel Montaigne (1580), Essays [1]

“I, too, have long investigated, have gone through all arts and sciences. I became a theologian, consulted authorities, weighed all, tested all,—polemics, exegesis, dogmatism. All was babble: nothing breathed of divinity! I became a jurist, endeavored to become acquainted with justice, and learned how to distort justice. I found an idol, shaped by the hands of self-interest and self-conceit, a bastard of justice, not herself. I became a physician, intending to learn the human structure, and the methods of supporting it when it gives way; but I found not what I sought, — I only found the art of methodically murdering men. I became a philosopher, desiring to know the soul of man, to catch truth by the wings and wisdom by the forelock; and I found shadows, vapors, follies, bound into a system!”
— Faust (c.1770), Augsburg puppet-play version (see: Faustian) [6]

“The criticisms which have been hurled at me have not worried me. A man cannot control his beliefs. If he is honest in his frank expression of them, that is all that can in justice be required of him. Professor Thomson and a thousand others do not in the least agree with me. His criticism of me, as I read it, charged that because I doubted the soul's immortality, or 'personality,' as he called it, my mind must be abnormal, 'pathological,' in other, words, diseased. I greatly admire Thomson. What he said about my mind did not disturb me. I try to say exactly what I honestly believe to be the truth, and more than that no man can do. I honestly believe that creedists have built up a mighty structure of inaccuracy, based, curiously, on those fundamental truths which I, with every honest man, must not alone admit but earnestly acclaim.”
— Thomas Edison (1910), response to his controversial 1910 New York Times soul-denying interview [2]

“I was raised Catholic, [but] I’m pretty much agnostic at this point in my life. But I find atheism just as hard to get my head around as I find fundamental Christianity. Because if there is no such thing as cosmic justice, what is the point of being good? [see: Jeffrey Dahmer] I feel some sort of need for biblical atonement, or justice, or something. I like to believe there is some comeuppance, that karma kicks in at some point, even if it takes years or decades to happen. My girlfriend says this great thing that’s become my philosophy as well. ‘I want to believe there’s a heaven. But I can’t not believe there’s a hell.’”
— Vince Gilligan (2011), NY Times interview on Breaking Bad [2]

“Our taste for justice is a useful illusion.”
— Joshua Greene (2013), commentary on the Nichols-Knobe determinism study [5]

References
1. (a) Montaigne, Michel. (1580). The Essays of Montaigne (translator: E.J. Trechmann) (Book 2, Ch. 12, pg. 494). Publisher, 1927.
(b) Henderson, Lawrence J. (1935). Pareto’s General Sociology: A Physiologists Interpretation (pg. 33). Harvard University Press.
2. Edison, Thomas. (1911). “Thomas A. Edison on Immortality: the Great Inventor Declares Immortality of the Soul Improbable” (doc) (Interview by Edward Marshall), The Columbian Magazine, 3(4), Jan.
3. Lindsay, Robert B. (1983). “Social Exemplifications of Physical Principles”; in: Old and New Questions in Physics, Cosmology, Philosophy, and Theoretical Biology: Essays in Honor of Wolfgang Yourgrau (editor: Alwyn Merwe) (§B7:647-58; Bohr, pg. 654). Plenum Press.
4. Harris, Sam. (2010). The Moral Landscape: How Science can Determine Human Values (pg. 106) Free Press.
5. Greene, Joshua. (2013). Moral Tribes: Emotion, Reason, and the Gap Between Us and Them (pg. #). Penguin.
6. Goethe, Johann. (1832). Faust (translator: Bayard Taylor) (pgs. 230-31). Houghton, Mifflin & Co., 1883.
7. (a) Feeley, Michael. (1983). Court Reform on Trial (pg. 184). Basic Books.
(b) Walker, Samuel. (2014). Sense and Nonsense About Crime, Drugs, and Communities (§:Justice Thermodynamics, pgs. 74-75). Cengage Learning.
8. Walker, Samuel. (2014). Sense and Nonsense About Crime, Drugs, and Communities (§:Justice Thermodynamics, pgs. 74-75). Cengage Learning.
9. Empedocles. (435BC). The Poem of Empedocles: a Text and Translation with an Introduction (editor: Brad Inwood) (pg. 139). University of Toronto Press, 1992.
10. Taylor, C.C.W. (1999). The Atomists: Leucippus and Democritus: Fragments: a Text and Translation with a Commentary by C.C.W. Taylor (pg. 3, 5). University of Toronto Press.

Further reading
● Carver, Thomas N. (1915). Essays in Social Justice (pgs. 132-35; energy, 35+ pgs). Harvard University Press.

External links
● Justice – Wikipedia.

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