A pdf version of this article is available here – Heraclitus-Fragment80
Some Notes on Πόλεμος and Δίκη in Heraclitus B80
εἰδέναι δὲ χρὴ τὸν πόλεμον ἐόντα ξυνόν, καὶ δίκην ἔριν, καὶ γινόμενα πάντα κατ΄ ἔριν καὶ χρεώμενα [χρεών]. Fragmentum 80.
This fragment, attributed to Heraclitus, is generally considered to mean something rather abstract such as: war is everywhere and strife is justice and all that is arises and passes away because of strife.
That is, πόλεμος is regarded as a synonym for either kampf, or more generally, for war. However, I incline toward the view that this older understanding of – the accepted rendition of – πόλεμος is a misinterpretation , and that rather than kampf (struggle), or a general type of strife, or what we now associate with the term war, πόλεμος implies what I have elsewhere termed the acausality (a simultaneity)  beyond our causal ideation, and which ideation has separated object from subject, and often abstracted them into seemingly conflicting opposites . Hence my particular interpretation of Fragmentum 53:
Πόλεμος πάντων μὲν πατήρ ἐστι, πάντων δὲ βασιλεύς, καὶ τοὺς μὲν θεοὺς ἔδειξε τοὺς δὲ ἀνθρώπους, τοὺς μὲν δούλους ἐποίησε τοὺς δὲ ἐλευθέρους.
Polemos our genesis, governing us all to bring forth some gods, some mortal beings with some unfettered yet others kept bound.
Hence my interpretation of Fragment 80 – εἰδέναι δὲ χρὴ τὸν πόλεμον ἐόντα ξυνόν, καὶ δίκην ἔριν, καὶ γινόμενα πάντα κατ΄ ἔριν καὶ χρεώμενα [χρεών] – as:
One should be aware that Polemos pervades, with discord δίκη, and that beings are naturally born by discord. 
Here, I have deliberately transliterated (instead of translated) πόλεμος, and left δίκη as δίκη – because both πόλεμος and δίκη (written Πόλεμος and, I suggest, Δίκα) should be regarded, like ψυχή (psyche/Psyche) as terms or as principles in their own right (hence the capitalization), and thus imply, suggest, and require, interpretation and explanation, something especially true, in my opinion, regarding Δίκα. To render them blandly by English terms such as ‘war’ and ‘justice’ – which have their own now particular meaning(s) – is in my view erroneous and somewhat lackadaisical. δίκη for instance could be, depending on context: the custom(s) of a folk, judgement (or Judgement personified), the natural and the necessary balance, the correct/customary/ancestral way, and so on.
In respect of Δίκα, I write it thus to intimate a new, a particular and numinous, philosophical principle, and differentiate it from the more general δίκη. As a numinous principle, or axiom, Δίκα thus suggests what lies beyond and what was the genesis of δίκη personified as the goddess, Judgement – the goddess of natural balance, of the ancestral way and ancestral customs.
Thus, Δίκα implies the balance, the reasoned judgement, the thoughtful reasoning – σωφρονεῖν – that πάθει μάθος brings and restores, and which accumulated πάθει μάθος of a particular folk or πόλις forms the basis for their ancestral customs. δίκη is therefore, as the numinous principle Δίκα, what may be said to be a particular and a necessary balance between ἀρετή and ὕβρις – between the ὕβρις that often results when the personal, the natural, quest for ἀρετή becomes unbalanced and excessive.
That is, when ἔρις (discord) is or becomes δίκη – as suggested by Heraclitus in Fragment 80.
In respect of Πόλεμος, it is perhaps interesting that in the recounted tales of Greek mythology attributed to Aesop, and in circulation at the time of Heraclitus, a personified πόλεμος (as the δαίμων of kindred strife) married a personified ὕβρις (as the δαίμων of arrogant pride)  and that it was a common folk belief that πόλεμος accompanied ὕβρις – that is, that Polemos followed Hubris around rather than vice versa, causing or bringing ἔρις.
As a result of ἔρις, there often arises πάθει μάθος – that practical and personal knowing, that reasoned understanding which, according to Aeschylus  is the new law, the new understanding, given by Zeus to replace the older more religious and dogmatic way of fear and dread, often viewed as Μοῖραι τρίμορφοι μνήμονές τ᾽ Ἐρινύες . A new understanding which Aeschylus saught to explain in the Oresteia.
Therefore one can perhaps understand and appreciate the true and acausal nature of Πόλεμος which, as suggested by Fragment 53, is a natural principle (or ‘energy’ or a manifestation of Being) which affects, or governs, all mortals and which, as suggested by Fragment 80, causes the manifestation of beings from Being (the causal separation of beings) and which natural separation results in ἔρις and thence, as suggested by Fragment 123  a return to Being; a return which can result, as suggested by Fragment 112  arise from thoughtful reasoning [σωφρονεῖν] – and which thoughtful, balanced, reasoning can incline us toward not committing ὕβρις.
April 2011 CE
 For the axiom of acausality, see my Introduction to The Philosophy of The Numen.
 For an outline of opposites, refer to my essay The Abstraction of Change as Opposites and Dialectic.
 Some alternative renderings of this fragment are:
One should be aware that polemos is pervasive; and discord δίκη, and that beings [our being] quite naturally come-into-being through discord
One should be aware that polemos pervades; with discord δίκη, and that all beings are begotten because of discord.
 A δαίμων is not one of the pantheon of major Greek gods – θεοί – but rather a lesser type of divinity who might be assigned by those gods to bring good fortune or misfortune to human beings and/or watch over certain human beings and especially particular numinous (sacred) places.
Furthermore, Polemos was originally the δαίμων of kindred strife, whether familial, or of one’s πόλις (one’s clan and their places of dwelling). Thus, to describe Polemos, as is sometimes done, as the god of conflict (or war), is doubly incorrect.
 Agamemnon,174-183. qv. my essay, From Aeschylus To The Numinous Way – The Numinous Authority of πάθει μάθος
 Aeschylus (attributed), Prometheus Bound, 515-6
 Φύσις κρύπτεσθαι φιλεῖ – Concealment accompanies Physis. See my Physis, Nature, Concealment, and Natural Change.
 σωφρονεῖν ἀρετὴ μεγίστη, καὶ σοφίη ἀληθέα λέγειν καὶ ποιεῖν κατὰ φύσιν ἐπαίοντας
For this fragment, see my essay The Balance of Physis – Notes on λόγος and ἀληθέα in Heraclitus.