Quantum Thermodynamic Selection
The Central Claim
Decoherence rates in thermodynamic environments scale with free energy differences:
Γᵢ = Γ₀ · exp(ΔGᵢ/kT)
This yields selection probabilities:
P(i) ∝ |αᵢ|² · exp(−ΔGᵢ/kT)
This may already be implicit in standard decoherence theory. I'm looking to either:
- Verify this is derivable from Born-Markov/Redfield equations with thermal bath
- Identify where it differs and design experiments to test
Theoretical Basis - Starting Point: Path Integral + Wick Rotation
The Euclidean path integral:
ψ[path] ∝ exp(−S_E/ℏ)
is mathematically identical to the partition function:
Z ∝ Σ exp(−E/kT)
Standard interpretation: This is a calculational tool (Wick rotation t → −iτ).
Proposed interpretation: This connection is physical. During decoherence, environmental coupling forces quantum amplitudes to thermally weight by free energy.
Question: Can we derive Γᵢ ∝ exp(ΔGᵢ/kT) from:
dρ_S/dt = −i[H_S, ρ_S] + Σᵢⱼ γᵢⱼ(Lᵢⱼ ρ_S Lᵢⱼ† − ½{Lᵢⱼ†Lᵢⱼ, ρ_S})
where γᵢⱼ couples to thermal bath at temperature T?
Expected Derivation Path
For system + thermal environment:
- System-bath coupling: H_I couples to environment with temperature T
- Born-Markov approximation: Assume weak coupling, Markovian bath
- Thermal state of bath: ρ_B ∝ exp(−H_B/kT)
- Trace over bath: Lindblad operators depend on thermal occupation
Prediction: Decoherence rates γᵢⱼ should contain exp(±ΔE/kT) factors from bath thermal statistics.
Question: Does this naturally give γ ∝ exp(ΔG/kT) where ΔG includes entropic contributions?
Why This Matters: The ΔG ~ kT Regime
Standard decoherence theory focuses on:
- Strong coupling: Rapid decoherence, classical behavior
- Weak coupling: Slow decoherence, quantum behavior
This framework highlights the intermediate regime ΔG ~ kT where:
- Decoherence rate varies exponentially with ΔG
- Smooth quantum-classical interpolation
- Biology operates here
Testable Predictions in Accessible Systems
Molecular dyads in solution (we can measure this now):
- Vary ΔG via solvent polarity, molecular structure
- Vary T from 77K to 350K
- Measure coherence time via 2D electronic spectroscopy
- Prediction: log(Γ) vs. ΔG/kT should be linear, slope = 1
Protein cavity engineering:
- Mutate photosynthetic protein to alter ΔG landscape
- Keep chromophore energetics constant
- Measure coherence lifetimes
- Prediction: τ_coherence ∝ exp(−ΔG/kT)
How You Can Help
1. Theoretical Verification
Can you derive (or show where it's already derived):
Γᵢ ∝ exp(ΔGᵢ/kT)
from standard master equation with thermal bath?
If yes: This formalizes existing physics. Useful framework.
If no: This is new hypothesis. Needs experimental test.
2. Critical Evaluation
Where does this framework:
- Agree with standard decoherence theory?
- Extend standard theory with new predictions?
- Conflict with established results?
Relationship to Existing Work
Einselection (Zurek)
Standard: Environment selects pointer states
This framework: ΔG/kT determines which states are robust pointers
Relationship: Potentially same physics, made quantitative
Quantum Biology (Engel, Lambert, etc.)
Standard: Quantum effects in biology when protein environment structured
This framework: Structure creates favorable ΔG landscape, enabling coherence
Relationship: Mechanistic explanation for empirical observations
Decoherence Theory (Joos, Zeh, Caldeira-Leggett)
Standard: System-bath coupling causes decoherence
This framework: Thermal bath weights rates by ΔG/kT
Relationship: May be implicit in detailed calculations, now made explicit
Open Questions
- Is Γ ∝ exp(ΔG/kT) derivable from standard theory?
- If yes: Show me the calculation
- If no: How do we test it experimentally?
- Does this work at T = 0?
- Framework requires thermal bath
- What happens in quantum regime kT → 0?
- Is this supplementary to QM or fundamental?
- What about many-body effects?
- Framework stated for individual states
- How does it extend to entangled systems?
- Collective modes?
- Connection to quantum thermodynamics?
- Recent field studying quantum + thermodynamic together
- How does this relate to fluctuation theorems, Jarzynski equality, etc.?
Thanks for taking a look!
