Second Death in John's Writings

The phrase "second death" appears in four verses in Revelation:

Revelation 2:11 [KJV] He that hath an ear, let him hear what the Spirit saith unto the churches; He that overcometh shall not be hurt of the second death.

NA28 Ὁ ἔχων οὖς ἀκουσάτω τί τὸ πνεῦμα λέγει ταῖς ἐκκλησίαις. Ὁ νικῶν οὐ μὴ ἀδικηθῇ ἐκ τοῦ θανάτου τοῦ δευτέρου.

There does not seem to be any significant textual difference between the so-called Textus Receptus and the NA28 at Revelation 2:11.

To be hurt or injured (ἀδικηθῇ) by the second death is already some hint at what the second death constitutes.  However, it is necessarily a bit vague.  In the New Testament, it is not used of annihilation or even conventional death.  It often refers to receiving an injustice, though in this case it seems to relate more to physical harm as in Revelation 9:10 with the scorpions.

Thus, the second death is portrayed has having the ability to injure people (though not those who overcome).

Revelation 20:6 [KJV] Blessed and holy [is] he that hath part in the first resurrection: on such the second death hath no power, but they shall be priests of God and of Christ, and shall reign with him a thousand years.

NA28 μακάριος καὶ ἅγιος ὁ ἔχων μέρος ἐν τῇ ἀναστάσει τῇ πρώτῃ· ἐπὶ τούτων ὁ δεύτερος θάνατος οὐκ ἔχει ἐξουσίαν, ἀλλ’ ἔσονται ἱερεῖς τοῦ θεοῦ καὶ τοῦ Χριστοῦ καὶ βασιλεύσουσιν μετ’ αὐτοῦ [τὰ] χίλια ἔτη.

The TR has "ὁ θάνατος ὁ δεύτερος" instead of "ὁ δεύτερος θάνατος" and does not include the bracketed [τὰ].  The meaning seems to be the same. 

The word "power" here is part of the coordinated words ἐξουσίαν and ἐπὶ, which together refer to having "power over" something, effectively a question of authority or jurisdiction.  The angel that had "power over" fire is mentioned in Revelation 14:18 and God is said to have "power over" the plagues in Revelation 16:9, for example. 

Thus, the second death is portrayed has having effectively a jurisdiction, or authority, though not over those who are part of the first resurrection.

Revelation 20:14 [KJV] And death and hell were cast into the lake of fire. This is the second death.

NA28 καὶ ὁ θάνατος καὶ ὁ ᾅδης ἐβλήθησαν εἰς τὴν λίμνην τοῦ πυρός. οὗτος ὁ θάνατος ὁ δεύτερός ἐστιν, ἡ λίμνη τοῦ πυρός. 

The TR (of the KJV) has "οὗτος ἐστιν ὁ δεύτερός θάνατος" (this is the second death) rather than "this second death is the lake of fire" (my translation of the NA28).  I have not carefully studied the textual evidence for the difference between the readings.

Under either reading, the sentence serves to explain what the "second death" is with reference to the lake of fire, as opposed to the opposite.

Revelation 21:8 [KJV] But the fearful, and unbelieving, and the abominable, and murderers, and whoremongers, and sorcerers, and idolaters, and all liars, shall have their part in the lake which burneth with fire and brimstone: which is the second death.

NA28 τοῖς δὲ δειλοῖς καὶ ἀπίστοις καὶ ἐβδελυγμένοις καὶ φονεῦσιν καὶ πόρνοις καὶ φαρμάκοις καὶ εἰδωλολάτραις καὶ πᾶσιν τοῖς ψευδέσιν τὸ μέρος αὐτῶν ἐν τῇ λίμνῃ τῇ καιομένῃ πυρὶ καὶ θείῳ, ὅ ἐστιν ὁ θάνατος ὁ δεύτερος.

TR δειλοῖς δὲ καὶ ἀπίστοις καὶ ἐβδελυγμένοις καὶ φονεῦσιν καὶ πόρνοις καὶ φαρμακεῦσιν καὶ εἰδωλολάτραις καὶ πᾶσιν τοῖς ψευδέσιν τὸ μέρος αὐτῶν ἐν τῇ λίμνῃ τῇ καιομένῃ πυρὶ καὶ θείῳ ὅ ἐστιν δεύτερος θάνατος

While there are some minor differences between the NA28 and TR text, it seems that the relevant phrase, "ὅ ἐστιν ὁ θάνατος ὁ δεύτερος," is essentially the same between them (regardless of whether the articles should be present or not, a question I have not yet carefully examined).

In Revelation:

• John uses "ὅ ἐστιν" in Revelation 2:7 to introduce an explanation of the location of the tree of life;
• John uses "ὅ ἐστιν" in Revelation 20:12 to explain which book was opened; and
• John uses "ὅ ἐστιν" in Revelation 21:17 to associate the 144 cubit measurement "of a man" is "of an angel."

Based on such usage, the most we can say is that like TR Revelation 20:14, the point seems to be link the "lake of fire" and the "second death."