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The impressive applications of TCT demand answers to fundamental questions such as how is TCT connected to the thermodynamics of liquids and glasses and how to formulate TCT from the first‐principles statistical physics of potential‐energy landscapes of liquids and glasses. This is an area that has not received much attention so far except for the work of Naumis and coworkers [13, 32] that we summarize in this section.

Naumis uses simple harmonic potentials to express the Hamiltonian (H) of a floppy system as follows:

(24)

Here, x_f is the fraction of floppy modes (= f/3); p_j and q_j are, respectively, the momentum and position coordinates of oscillators representing vibrational modes of frequency ω_j and floppy modes of frequency ω_o. For real systems, one has to use more sophisticated interaction potentials. Nonetheless, a harmonic model gives a reasonable qualitative feel of the thermodynamics of the floppy modes. Naumis assigns a small but finite frequency ω_o (<<ω_vib) to each floppy mode. The equilibrium thermodynamics of this Hamiltonian can be calculated easily. The result for the internal energy U of the system is

(25)

Here, D is the well‐known Debye function and ω_D is the Debye frequency. According to Naumis, the expression for entropy is as follows:

(26)

The last terms in Eqs. (25) and (26) represent the contributions of the floppy modes and constitute the configurational energy and entropy, respectively. As discussed in Section 5.2, the configurational entropy is proportional to f.

From Eq. (25), the configurational heat capacity, ΔC_V, is given by

(27)

where x = h ω_o/kT.

As Naumis has pointed out, the physical picture in the PEL is clear. Since ω_o is small, the curvatures of the potential energy surface at the inherent structures are small in the floppy directions. Naumis refers to these directions as channels in the landscape. The landscape is flatter in these channels, thus allowing greater configurational entropy and greater structural freedom upon increase in T and thus greater fragility.