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An Information-theoretic Collective Variable for Configurational Entropy

Ashley Z. Guo, Kaelyn Chang, Nicholas J. Corrente

Abstract

Entropy governs molecular self-assembly, phase transitions, and material stability, yet remains challenging to quantify and directly control in molecular systems. Here, we demonstrate that the computable information density (CID), a data compression-based information theoretic metric, provides an instantaneous general measure of configurational entropy in molecular dynamics simulations, reflecting both local and long-range structural organization. We validate the CID across systems of increasing complexity, beginning with single-component Lennard-Jones melting before examining binary phase separation, polymer condensation and dispersion, and assembly of amorphous carbon networks at multiple densities. Unlike conventional order parameters, CID requires no a priori knowledge of relevant structural features and captures entropic signatures across a variety of molecular systems and discretization resolutions. By establishing entropy as a directly accessible structural metric, this framework lays a foundation for future entropy-driven materials design and optimization strategies.

An Information-theoretic Collective Variable for Configurational Entropy

Abstract

Entropy governs molecular self-assembly, phase transitions, and material stability, yet remains challenging to quantify and directly control in molecular systems. Here, we demonstrate that the computable information density (CID), a data compression-based information theoretic metric, provides an instantaneous general measure of configurational entropy in molecular dynamics simulations, reflecting both local and long-range structural organization. We validate the CID across systems of increasing complexity, beginning with single-component Lennard-Jones melting before examining binary phase separation, polymer condensation and dispersion, and assembly of amorphous carbon networks at multiple densities. Unlike conventional order parameters, CID requires no a priori knowledge of relevant structural features and captures entropic signatures across a variety of molecular systems and discretization resolutions. By establishing entropy as a directly accessible structural metric, this framework lays a foundation for future entropy-driven materials design and optimization strategies.
Paper Structure (16 sections, 3 equations, 7 figures, 1 table)

This paper contains 16 sections, 3 equations, 7 figures, 1 table.

Table of Contents

  1. Introduction
  2. Methods
  3. Computable Information Density (CID)
  4. Entropy from Radial Distribution Functions
  5. Molecular Dynamics Simulations
  6. Lennard-Jones Single-Component Melting
  7. Lennard-Jones Binary Phase Separation
  8. Coarse-grained Homopolymer System
  9. Carbon Systems
  10. Results and Discussion
  11. Single-component Lennard-Jones Fluid
  12. Binary Lennard-Jones Fluid
  13. Homopolymer Phase Transitions
  14. Amorphous Carbons
  15. Sensitivity to Discretization
  16. ...and 1 more sections

Figures (7)

  • Figure 1: Schematic of the CID framework. Atomic coordinates are discretized onto a 3D grid, mapped to a 1D sequence via a Hilbert curve, and compressed using LZ77. CID is calculated as the normalized ratio of compressed to original sequence length, with lower values indicating more ordered (lower entropy) configurations.
  • Figure 2: Computable information density tracks Lennard-Jones melting transition. (A) Representative snapshots showing FCC crystal (frame 0, $T^* = 0.01$), onset of melting (frame 200, $T^* = 0.4$), mid-transition (frame 400, $T^* = 0.75$), and equilibrated liquid (frame 1200, $T^* = 1.5$). (B) CID (blue) and temperature (red) evolution during linear heating. CID rises sharply between frames 100-600 as crystalline order breaks down. (C) Comparison of structural metrics: CID (blue), pair correlation entropy $S_2$ (orange), and bond-orientational order parameter $Q_6$ (green). Both entropy metrics increase during melting while $Q_6$ decreases, but CID shows more gradual evolution reflecting sensitivity to multi-scale structural features. Profiles represent averages over 5 independent simulation runs, with shaded regions indicating one standard deviation.
  • Figure 3: Correlations between structural metrics during Lennard-Jones melting (frames 100-600). Scatter plots show relationships between (A) CID vs $Q_6$ ($R^2 = 0.897$), (B) $S_2$ vs $Q_6$ ($R^2 = 0.436$), and (C) CID vs $S_2$ ($R^2 = 0.633$). CID correlates strongly with bond-orientational order while maintaining distinct, nonlinear relationship with pair correlation entropy. Each point represents a single MD snapshot during the melting transition.
  • Figure 4: CID and $S_2$ track phase separation and distinguish morphologies in binary LJ mixtures. (A) Representative snapshots showing well mixed binary system at high temperature, transient structures, and both slab and bicontinuous phase separated configurations observed at low temperature. (B) CID evolution during equilibration (frames 70-100, T* = 5.0), quench (frame 100), and re-equilibration (frames 100-200, T* = 1.0). The peak in CID near frame 100 reflects NPT volume adjustment. Slab morphologies (blue) converge to lower CID than bicontinuous structures (orange). (C) Pair correlation entropy $S_2$ evolution over frames 70-200 shows similar trends to CID but with larger morphology-dependent separation and greater variance within each morphology class, demonstrating CID's complementary sensitivity to global spatial patterns rather than local radial correlations.
  • Figure 5: Homopolymer structural transitions captured by CID. (A) Simulation snapshots showing dispersed and condensed states at different temperatures with corresponding frame numbers. (B) Normalized CID (blue) and temperature (red) evolution throughout thermal cycling. CID decreases during condensation and increases upon re-dispersion, tracking entropy changes without polymer-specific order parameters. Each plotted profile is the mean over 5 independent simulations, with one standard deviation shown in the shaded region.
  • ...and 2 more figures