X. THERMODYNAMICS · Partition function: Z

Read the equation

This relation defines Partition function: Z in the source section “X. THERMODYNAMICS · Partition function: Z”. Applies an exponential factor. The exponent determines its real scaling or, for a complex exponent, its phase. Its interpretation depends on the source’s stated variables and conditions; this record does not assign an unprovided physical or cognitive meaning to them.

Terms & definitions

The recovered passage does not supply a separate symbol table. Read the source context for the notation used in this version; familiar letters may carry different meanings in other builds.

How it works

1. Read Partition function: Z as the quantity being defined or updated by this relation.

2. Applies an exponential factor. The exponent determines its real scaling or, for a complex exponent, its phase.

3. Use this version’s variable definitions and update order. The same symbol may be assigned a different meaning in another build.

Assumptions & limits

• This source expression was recovered from the pinned code revision. Its presence does not establish that the associated program was built, run, or scientifically validated.

Original context

    explicit Thermodynamics(double T = 300.0) : temperature_(T) {}

    // 10.6-periodic weighting function
    static double theta_10_6(double config_param) {
        return std::exp(-std::pow(std::fmod(config_param, BASE_PAIRS_PER_TURN), 2) / 2.0);
    }

    // Partition function: Z = Σ exp(-E/k_B T) · Θ(10.6)
    double partition_function(const std::vector<double>& energies,
                             const std::vector<double>& config_params) const {
        double Z = 0.0;
        for (size_t i = 0; i < energies.size(); ++i) {
            double boltzmann = std::exp(-energies[i] / (kB * temperature_));
            double weight = theta_10_6(config_params[i]);
            Z += boltzmann * weight;
        }
        return Z;
    }

Partition function: Z = Σ exp(-E/k_B T) · Θ(10.6)

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