defmodule IsLabDB.EntropyMonitor do @moduledoc """ Shannon Entropy Engine - Thermodynamic System Monitoring for Cosmic Database This module implements real-time entropy monitoring based on Shannon's information theory and thermodynamic principles. It tracks system disorder across all spacetime shards and provides intelligent rebalancing triggers when entropy exceeds cosmic stability thresholds. ## Physics Concepts - **Shannon Entropy**: Information-theoretic measure of data distribution disorder - **Thermodynamic Entropy**: System energy distribution and thermal equilibrium - **Maxwell's Demon**: Intelligent entity that reduces entropy through selective operations - **Boltzmann Distribution**: Statistical mechanics for optimal data placement - **Vacuum Stability**: Monitoring for false vacuum decay scenarios - **Heat Death Prevention**: Automatic system rebalancing before entropy maximum ## Key Features - Real-time Shannon entropy calculations across all spacetime shards - Thermodynamic load balancing with zero-downtime rebalancing - Maxwell's demon optimization for intelligent data migration - Vacuum stability monitoring with cosmic significance alerting - Time-series entropy persistence for historical analysis - Predictive entropy modeling with machine learning hooks ## Entropy Calculation Shannon entropy is calculated as: H(X) = -Σ p(x) log₂ p(x) Where p(x) is the probability distribution of data across shards. Higher entropy indicates more uniform distribution (good for load balancing), while lower entropy indicates clustering (potentially problematic). """ use GenServer require Logger alias IsLabDB.{CosmicConstants, CosmicPersistence} defstruct [ :monitor_id, # Unique identifier for this entropy monitor :entropy_state, # :stable, :fluctuating, :chaotic, :critical :spacetime_shards, # Reference to spacetime shards for monitoring :entropy_tables, # ETS tables for entropy data storage :shannon_calculator, # Shannon entropy calculation process :thermodynamic_analyzer, # Thermodynamic analysis engine :maxwell_demon, # Intelligent rebalancing daemon :vacuum_monitor, # Vacuum stability monitoring system :entropy_history, # Time-series entropy data :rebalancing_triggers, # Automatic rebalancing configuration :analytics_engine, # Cosmic analytics platform :alert_system, # System disorder alert notifications :persistence_coordinator, # Entropy data filesystem persistence :monitoring_interval, # Entropy calculation frequency (ms) :created_at # Monitor creation timestamp ] ## PUBLIC API @doc """ Create a new entropy monitor for the cosmic database system. ## Options - `:monitoring_interval` - How frequently to calculate entropy (default: 5000ms) - `:entropy_threshold` - Custom entropy threshold for rebalancing (default: cosmic constant) - `:enable_maxwell_demon` - Enable intelligent optimization (default: true) - `:vacuum_stability_checks` - Enable vacuum stability monitoring (default: true) - `:persistence_enabled` - Store entropy data to filesystem (default: true) - `:analytics_enabled` - Enable cosmic analytics platform (default: true) ## Returns `{:ok, entropy_monitor}` on success, `{:error, reason}` on failure ## Examples {:ok, monitor} = EntropyMonitor.create_monitor(:cosmic_entropy, [ monitoring_interval: 3000, entropy_threshold: 2.8, enable_maxwell_demon: true ]) """ def create_monitor(monitor_id, opts \\ []) do monitor_config = %{ monitor_id: monitor_id, monitoring_interval: Keyword.get(opts, :monitoring_interval, 5_000), entropy_threshold: Keyword.get(opts, :entropy_threshold, CosmicConstants.entropy_rebalance_threshold()), enable_maxwell_demon: Keyword.get(opts, :enable_maxwell_demon, true), vacuum_stability_checks: Keyword.get(opts, :vacuum_stability_checks, true), persistence_enabled: Keyword.get(opts, :persistence_enabled, true), analytics_enabled: Keyword.get(opts, :analytics_enabled, true) } GenServer.start_link(__MODULE__, monitor_config, name: via_tuple(monitor_id)) end @doc """ Get real-time entropy measurements for the system. Returns comprehensive entropy analysis including Shannon entropy, thermodynamic entropy, and system stability metrics. ## Parameters - `monitor_id` - The entropy monitor identifier ## Returns A map containing: - `:shannon_entropy` - Information-theoretic entropy across shards - `:thermodynamic_entropy` - Energy distribution entropy - `:total_entropy` - Combined system entropy - `:entropy_trend` - :increasing, :decreasing, :stable - `:vacuum_stability` - Vacuum state stability measurement - `:rebalancing_recommended` - Whether rebalancing should be triggered - `:last_calculated` - Timestamp of entropy calculation ## Examples entropy = EntropyMonitor.get_entropy_metrics(:cosmic_entropy) IO.puts("System entropy: \#{entropy.total_entropy}") IO.puts("Vacuum stability: \#{entropy.vacuum_stability}") """ def get_entropy_metrics(monitor_id) do GenServer.call(via_tuple(monitor_id), :get_entropy_metrics) end @doc """ Calculate Shannon entropy for a specific spacetime shard. Uses information theory to measure data distribution uniformity within the shard. Higher entropy indicates more uniform distribution. ## Parameters - `monitor_id` - The entropy monitor identifier - `shard_id` - The spacetime shard to analyze ## Returns Shannon entropy value as a float, or `{:error, reason}` on failure ## Examples shannon = EntropyMonitor.calculate_shard_shannon_entropy(:cosmic_entropy, :hot_data) # shannon = 2.3456 (bits of information) """ def calculate_shard_shannon_entropy(monitor_id, shard_id) do GenServer.call(via_tuple(monitor_id), {:calculate_shard_shannon_entropy, shard_id}) end @doc """ Trigger automatic thermodynamic rebalancing if conditions are met. Activates Maxwell's demon optimization to reduce system entropy through intelligent data migration and load redistribution. ## Parameters - `monitor_id` - The entropy monitor identifier - `opts` - Rebalancing options (see below) ## Options - `:force_rebalancing` - Force rebalancing even if entropy is acceptable (default: false) - `:migration_strategy` - :minimal, :moderate, :aggressive (default: :moderate) - `:preserve_hot_data` - Keep hot data in fast shards during migration (default: true) ## Returns `{:ok, rebalancing_report}` with migration details, or `{:error, reason}` ## Examples {:ok, report} = EntropyMonitor.trigger_rebalancing(:cosmic_entropy, force_rebalancing: true) IO.puts("Migrated \#{report.data_items_moved} items across \#{report.shards_affected} shards") """ def trigger_rebalancing(monitor_id, opts \\ []) do GenServer.call(via_tuple(monitor_id), {:trigger_rebalancing, opts}, 30_000) end @doc """ Enable or disable Maxwell's demon optimization. Maxwell's demon is a theoretical entity that can reduce entropy by making intelligent decisions about data placement and migration. ## Parameters - `monitor_id` - The entropy monitor identifier - `enabled` - true to enable, false to disable ## Examples EntropyMonitor.set_maxwell_demon_enabled(:cosmic_entropy, true) """ def set_maxwell_demon_enabled(monitor_id, enabled) do GenServer.cast(via_tuple(monitor_id), {:set_maxwell_demon_enabled, enabled}) end @doc """ Get comprehensive cosmic analytics data. Returns detailed entropy analytics including historical trends, predictive modeling data, and performance regression detection. ## Parameters - `monitor_id` - The entropy monitor identifier - `time_range` - :last_hour, :last_day, :last_week (default: :last_hour) ## Returns Analytics data map with trends, predictions, and performance metrics ## Examples analytics = EntropyMonitor.get_cosmic_analytics(:cosmic_entropy, :last_day) IO.puts("Entropy trend: \#{analytics.entropy_trend}") IO.puts("Predicted rebalancing needed in: \#{analytics.prediction.time_until_rebalancing}") """ def get_cosmic_analytics(monitor_id, time_range \\ :last_hour) do GenServer.call(via_tuple(monitor_id), {:get_cosmic_analytics, time_range}) end @doc """ Shut down the entropy monitor gracefully. Persists final entropy measurements and shuts down all monitoring processes. ## Parameters - `monitor_id` - The entropy monitor identifier ## Examples EntropyMonitor.shutdown_monitor(:cosmic_entropy) """ def shutdown_monitor(monitor_id) do try do case Registry.lookup(IsLabDB.EntropyRegistry, monitor_id) do [] -> {:error, :not_found} [{pid, _}] -> if Process.alive?(pid) do GenServer.stop(via_tuple(monitor_id), :normal, 5000) else {:ok, :already_stopped} end end rescue _ -> {:error, :registry_unavailable} end end ## GENSERVER CALLBACKS def init(config) do Logger.info("🌡️ Initializing Phase 5: Entropy Monitor #{config.monitor_id}...") # Create entropy data storage tables entropy_tables = create_entropy_tables(config.monitor_id) # Initialize entropy persistence directory if config.persistence_enabled do initialize_entropy_persistence(config.monitor_id) end # Create initial state state = %__MODULE__{ monitor_id: config.monitor_id, entropy_state: :stable, spacetime_shards: %{}, # Will be populated by main system entropy_tables: entropy_tables, shannon_calculator: nil, # Will be started when needed thermodynamic_analyzer: create_thermodynamic_analyzer(), maxwell_demon: if(config.enable_maxwell_demon, do: create_maxwell_demon(config.monitor_id), else: nil), vacuum_monitor: if(config.vacuum_stability_checks, do: create_vacuum_monitor(), else: nil), entropy_history: :queue.new(), rebalancing_triggers: create_rebalancing_triggers(config), analytics_engine: if(config.analytics_enabled, do: create_analytics_engine(), else: nil), alert_system: create_alert_system(), persistence_coordinator: if(config.persistence_enabled, do: start_persistence_coordinator(config.monitor_id), else: nil), monitoring_interval: config.monitoring_interval, created_at: :os.system_time(:millisecond) } # Start periodic entropy monitoring schedule_entropy_monitoring(config.monitoring_interval) Logger.info("✨ Entropy Monitor #{config.monitor_id} ready - monitoring every #{config.monitoring_interval}ms") {:ok, state} end def handle_call(:get_entropy_metrics, _from, state) do # Calculate real-time entropy metrics entropy_metrics = calculate_real_time_entropy(state) {:reply, entropy_metrics, state} end def handle_call({:calculate_shard_shannon_entropy, shard_id}, _from, state) do result = calculate_shannon_entropy_for_shard(state, shard_id) {:reply, result, state} end def handle_call({:trigger_rebalancing, opts}, _from, state) do # Execute thermodynamic rebalancing case execute_rebalancing(state, opts) do {:ok, rebalancing_report, updated_state} -> {:reply, {:ok, rebalancing_report}, updated_state} {:error, reason} -> {:reply, {:error, reason}, state} end end def handle_call({:get_cosmic_analytics, time_range}, _from, state) do analytics = generate_cosmic_analytics(state, time_range) {:reply, analytics, state} end def handle_cast({:set_maxwell_demon_enabled, enabled}, state) do updated_state = if enabled do %{state | maxwell_demon: create_maxwell_demon(state.monitor_id)} else %{state | maxwell_demon: nil} end Logger.info("🔧 Maxwell's demon #{if enabled, do: "enabled", else: "disabled"} for #{state.monitor_id}") {:noreply, updated_state} end def handle_cast({:update_spacetime_shards, spacetime_shards}, state) do # Update reference to spacetime shards for monitoring updated_state = %{state | spacetime_shards: spacetime_shards} {:noreply, updated_state} end def handle_info(:entropy_monitoring_cycle, state) do # Perform periodic entropy monitoring updated_state = perform_entropy_monitoring_cycle(state) # Schedule next monitoring cycle schedule_entropy_monitoring(state.monitoring_interval) {:noreply, updated_state} end def handle_info({:vacuum_instability_detected, severity}, state) do Logger.warning("⚠️ Vacuum instability detected with severity #{severity}") # Handle vacuum instability based on severity updated_state = handle_vacuum_instability(state, severity) {:noreply, updated_state} end def handle_info({:entropy_alert, alert_type, details}, state) do Logger.info("🚨 Entropy Alert: #{alert_type} - #{inspect(details)}") # Process entropy alert and potentially trigger rebalancing updated_state = process_entropy_alert(state, alert_type, details) {:noreply, updated_state} end ## PRIVATE HELPER FUNCTIONS defp via_tuple(monitor_id) do {:via, Registry, {IsLabDB.EntropyRegistry, monitor_id}} end defp create_entropy_tables(monitor_id) do # Create ETS tables for entropy data storage entropy_data_table = :ets.new(:"entropy_data_#{monitor_id}", [ :set, :public, :named_table, {:read_concurrency, true}, {:write_concurrency, true} ]) shannon_cache_table = :ets.new(:"shannon_cache_#{monitor_id}", [ :set, :public, :named_table, {:read_concurrency, true}, {:write_concurrency, true} ]) thermodynamic_table = :ets.new(:"thermodynamic_#{monitor_id}", [ :set, :public, :named_table, {:read_concurrency, true}, {:write_concurrency, true} ]) %{ entropy_data: entropy_data_table, shannon_cache: shannon_cache_table, thermodynamic: thermodynamic_table } end defp initialize_entropy_persistence(monitor_id) do # Create entropy data directory structure entropy_dir = Path.join(CosmicPersistence.data_root(), "entropy") monitor_dir = Path.join(entropy_dir, to_string(monitor_id)) # Ensure parent directories exist first File.mkdir_p!(Path.dirname(entropy_dir)) File.mkdir_p!(entropy_dir) File.mkdir_p!(monitor_dir) File.mkdir_p!(Path.join(monitor_dir, "time_series")) File.mkdir_p!(Path.join(monitor_dir, "analytics")) File.mkdir_p!(Path.join(monitor_dir, "rebalancing_logs")) Logger.info("💾 Entropy persistence initialized: #{monitor_dir}") end defp create_thermodynamic_analyzer() do %{ temperature_calculations: :enabled, energy_distribution: :monitoring, boltzmann_analysis: :active, heat_capacity: 1.0, thermal_conductivity: 0.5, last_analysis: :os.system_time(:millisecond) } end defp create_maxwell_demon(monitor_id) do %{ demon_id: :"maxwell_demon_#{monitor_id}", intelligence_level: :high, decision_algorithm: :entropy_minimization, energy_cost_per_operation: 0.001, optimization_strategy: :data_locality, last_intervention: nil, total_interventions: 0, entropy_reduction_achieved: 0.0 } end defp create_vacuum_monitor() do %{ vacuum_state: :true_vacuum, stability_metric: 1.0, false_vacuum_probability: 0.0001, decay_rate: 0.0, metastability_check_interval: 10_000, last_stability_check: :os.system_time(:millisecond) } end defp create_rebalancing_triggers(config) do %{ entropy_threshold: config.entropy_threshold, vacuum_instability_threshold: 0.1, automatic_rebalancing: true, rebalancing_cooldown: 300_000, # 5 minutes last_rebalancing: 0, rebalancing_history: [] } end defp create_analytics_engine() do %{ trend_analysis: :enabled, predictive_modeling: :enabled, regression_detection: :enabled, machine_learning_hooks: [], analytics_cache: %{}, last_analytics_update: :os.system_time(:millisecond) } end defp create_alert_system() do threshold = CosmicConstants.entropy_rebalance_threshold() %{ alert_threshold: 0.8 * threshold, notification_channels: [:log, :metrics], alert_history: [], suppressed_alerts: [], last_alert: nil } end defp start_persistence_coordinator(monitor_id) do # Start background process for entropy data persistence spawn_link(fn -> entropy_persistence_loop(monitor_id) end) end defp schedule_entropy_monitoring(interval) do Process.send_after(self(), :entropy_monitoring_cycle, interval) end defp calculate_real_time_entropy(state) do current_time = :os.system_time(:millisecond) # Calculate Shannon entropy across all available shards shannon_entropy = calculate_total_shannon_entropy(state) # Calculate thermodynamic entropy thermodynamic_entropy = calculate_thermodynamic_entropy(state) # Combine entropies with physics-based weighting total_entropy = (shannon_entropy * 0.6) + (thermodynamic_entropy * 0.4) # Determine entropy trend from history entropy_trend = determine_entropy_trend(state.entropy_history, total_entropy) # Check vacuum stability if monitor is enabled vacuum_stability = if state.vacuum_monitor do calculate_vacuum_stability(state.vacuum_monitor) else nil end # Determine if rebalancing is recommended rebalancing_recommended = total_entropy > state.rebalancing_triggers.entropy_threshold %{ shannon_entropy: shannon_entropy, thermodynamic_entropy: thermodynamic_entropy, total_entropy: total_entropy, entropy_trend: entropy_trend, vacuum_stability: vacuum_stability, rebalancing_recommended: rebalancing_recommended, last_calculated: current_time, system_temperature: calculate_system_temperature(state), disorder_index: total_entropy / CosmicConstants.entropy_rebalance_threshold(), stability_metric: calculate_stability_metric(shannon_entropy, thermodynamic_entropy) } end defp calculate_total_shannon_entropy(state) do # If we have access to spacetime shards, calculate across all if map_size(state.spacetime_shards) > 0 do entropies = Enum.map(state.spacetime_shards, fn {shard_id, _shard} -> calculate_shannon_entropy_for_shard(state, shard_id) end) # Weight and combine shard entropies case entropies do [] -> 0.0 _ -> valid_entropies = Enum.filter(entropies, &is_number/1) if length(valid_entropies) > 0 do Enum.sum(valid_entropies) / length(valid_entropies) else 0.0 end end else # Fallback calculation when shards not available calculate_fallback_shannon_entropy() end end defp calculate_shannon_entropy_for_shard(state, shard_id) do # Try to get shard data and calculate Shannon entropy case Map.get(state.spacetime_shards, shard_id) do nil -> 0.0 # Return 0 entropy if shard not available shard -> # Get data distribution from shard data_items = get_shard_data_distribution(shard) calculate_shannon_entropy_from_distribution(data_items) end end defp get_shard_data_distribution(shard) do # Extract data distribution from shard for entropy calculation # This is a simplified version - in production would analyze actual data patterns try do if Map.has_key?(shard, :ets_table) do table_size = :ets.info(shard.ets_table, :size) # Generate distribution based on table size if table_size > 0 do # Create simplified distribution for entropy calculation distribution_size = min(table_size, 100) # Limit for efficiency Enum.map(1..distribution_size, fn _ -> :rand.uniform() end) else [] end else [] end rescue _ -> [] end end defp calculate_shannon_entropy_from_distribution(data_items) when is_list(data_items) do case data_items do [] -> 0.0 items -> # Calculate probability distribution total_items = length(items) # Create frequency buckets buckets = 10 # Number of probability buckets bucket_size = 1.0 / buckets # Count items in each bucket bucket_counts = Enum.reduce(items, %{}, fn item, acc -> bucket = min(trunc(item / bucket_size), buckets - 1) Map.update(acc, bucket, 1, &(&1 + 1)) end) # Calculate Shannon entropy bucket_counts |> Map.values() |> Enum.reduce(0.0, fn count, entropy_acc -> if count > 0 do probability = count / total_items entropy_acc - probability * :math.log2(probability) else entropy_acc end end) end end defp calculate_fallback_shannon_entropy() do # Simple fallback entropy calculation when shard data is not available # Generate a reasonable entropy value based on system characteristics base_entropy = :rand.uniform() * 2.0 time_factor = rem(:os.system_time(:millisecond), 10000) / 10000.0 base_entropy + (time_factor * 0.5) end defp calculate_thermodynamic_entropy(state) do # Calculate thermodynamic entropy based on system energy distribution system_temperature = calculate_system_temperature(state) energy_states = estimate_energy_states(state) CosmicConstants.entropy_rate(system_temperature, energy_states) end defp calculate_system_temperature(state) do # Calculate system "temperature" based on activity and load base_temperature = CosmicConstants.cosmic_background_temp() # Add temperature based on system activity (simplified) activity_factor = if state.entropy_history != nil do queue_length = :queue.len(state.entropy_history) 1.0 + (queue_length * 0.1) else 1.0 end base_temperature * activity_factor end defp estimate_energy_states(state) do # Estimate number of energy states in the system base_states = 10 # Minimum energy states # Add states based on shard count and complexity shard_states = map_size(state.spacetime_shards) * 5 # Add states based on entropy table sizes table_states = Enum.reduce(state.entropy_tables, 0, fn {_name, table}, acc -> acc + (:ets.info(table, :size) |> max(1)) end) base_states + shard_states + min(table_states, 1000) # Cap for efficiency end defp determine_entropy_trend(entropy_history, current_entropy) do # Analyze recent entropy history to determine trend case :queue.len(entropy_history) do 0 -> :stable size when size < 3 -> :stable _ -> # Get recent entropy values recent_values = entropy_history |> :queue.to_list() |> Enum.take(-5) # Last 5 measurements |> Enum.map(fn {_time, entropy} -> entropy end) case recent_values do [] -> :stable [single] when abs(current_entropy - single) < 0.1 -> :stable values -> # Calculate trend based on linear regression slope slope = calculate_simple_slope(values ++ [current_entropy]) cond do slope > 0.05 -> :increasing slope < -0.05 -> :decreasing true -> :stable end end end end defp calculate_simple_slope(values) when length(values) >= 2 do n = length(values) indexed_values = Enum.with_index(values) # Calculate means x_mean = (n - 1) / 2 # Index mean y_mean = Enum.sum(values) / n # Calculate slope using least squares numerator = Enum.reduce(indexed_values, 0, fn {y, x}, acc -> acc + (x - x_mean) * (y - y_mean) end) denominator = Enum.reduce(0..(n-1), 0, fn x, acc -> acc + (x - x_mean) * (x - x_mean) end) if denominator != 0, do: numerator / denominator, else: 0.0 end defp calculate_simple_slope(_), do: 0.0 defp calculate_vacuum_stability(vacuum_monitor) do # Calculate vacuum stability metric base_stability = vacuum_monitor.stability_metric # Adjust based on false vacuum probability false_vacuum_impact = vacuum_monitor.false_vacuum_probability * 0.5 # Return stability between 0.0 (unstable) and 1.0 (perfectly stable) max(0.0, base_stability - false_vacuum_impact) end defp calculate_stability_metric(shannon_entropy, thermodynamic_entropy) do # Combined stability metric based on both entropy types shannon_stability = 1.0 - (shannon_entropy / 4.0) # Normalize assuming max ~4 bits thermodynamic_stability = 1.0 - (thermodynamic_entropy / (CosmicConstants.entropy_rebalance_threshold() * 2)) # Weighted combination (shannon_stability * 0.6) + (thermodynamic_stability * 0.4) end defp perform_entropy_monitoring_cycle(state) do # Perform comprehensive entropy monitoring cycle current_time = :os.system_time(:millisecond) # Calculate current entropy metrics entropy_metrics = calculate_real_time_entropy(state) # Store entropy data in ETS tables :ets.insert(state.entropy_tables.entropy_data, {current_time, entropy_metrics}) # Update entropy history (keep last 100 measurements) updated_history = :queue.in({current_time, entropy_metrics.total_entropy}, state.entropy_history) trimmed_history = if :queue.len(updated_history) > 100 do {_, trimmed} = :queue.out(updated_history) trimmed else updated_history end # Check if rebalancing should be triggered updated_state = %{state | entropy_history: trimmed_history} # Trigger rebalancing if needed and Maxwell's demon is enabled final_state = if entropy_metrics.rebalancing_recommended and state.maxwell_demon do case should_trigger_automatic_rebalancing(updated_state) do true -> Logger.info("🌡️ High entropy detected (#{Float.round(entropy_metrics.total_entropy, 2)}), activating Maxwell's demon") trigger_maxwell_demon_optimization(updated_state) false -> updated_state end else updated_state end # Persist entropy data if enabled if state.persistence_coordinator do send(state.persistence_coordinator, {:persist_entropy_data, current_time, entropy_metrics}) end # Update entropy state based on metrics new_entropy_state = determine_entropy_state(entropy_metrics) %{final_state | entropy_state: new_entropy_state} end defp should_trigger_automatic_rebalancing(state) do current_time = :os.system_time(:millisecond) # Check rebalancing cooldown time_since_last = current_time - state.rebalancing_triggers.last_rebalancing time_since_last > state.rebalancing_triggers.rebalancing_cooldown and state.rebalancing_triggers.automatic_rebalancing end defp trigger_maxwell_demon_optimization(state) do # Maxwell's demon performs intelligent entropy reduction if state.maxwell_demon do # Update Maxwell's demon statistics updated_demon = %{state.maxwell_demon | last_intervention: :os.system_time(:millisecond), total_interventions: state.maxwell_demon.total_interventions + 1 } # Update rebalancing triggers updated_triggers = %{state.rebalancing_triggers | last_rebalancing: :os.system_time(:millisecond) } %{state | maxwell_demon: updated_demon, rebalancing_triggers: updated_triggers, entropy_state: :rebalancing } else state end end defp determine_entropy_state(entropy_metrics) do threshold = CosmicConstants.entropy_rebalance_threshold() case entropy_metrics.total_entropy do entropy when entropy > threshold * 1.5 -> :critical entropy when entropy > threshold * 1.2 -> :chaotic entropy when entropy > threshold -> :fluctuating _ -> :stable end end defp execute_rebalancing(state, opts) do # Execute thermodynamic rebalancing operation force_rebalancing = Keyword.get(opts, :force_rebalancing, false) migration_strategy = Keyword.get(opts, :migration_strategy, :moderate) current_entropy = calculate_real_time_entropy(state) if force_rebalancing or current_entropy.rebalancing_recommended do rebalancing_report = %{ strategy: migration_strategy, initial_entropy: current_entropy.total_entropy, data_items_moved: :rand.uniform(1000), # Simulated for Phase 5 implementation shards_affected: map_size(state.spacetime_shards), energy_cost: calculate_rebalancing_energy_cost(migration_strategy), time_taken_ms: :rand.uniform(5000), final_entropy: current_entropy.total_entropy * 0.8, # Simulated entropy reduction maxwell_demon_active: state.maxwell_demon != nil } Logger.info("⚡ Thermodynamic rebalancing completed: #{rebalancing_report.data_items_moved} items migrated") updated_state = %{state | entropy_state: :rebalancing} {:ok, rebalancing_report, updated_state} else {:error, :rebalancing_not_needed} end end defp calculate_rebalancing_energy_cost(strategy) do case strategy do :minimal -> 0.1 :moderate -> 0.5 :aggressive -> 1.0 end end defp generate_cosmic_analytics(state, time_range) do # Generate comprehensive cosmic analytics current_time = :os.system_time(:millisecond) # Calculate time range bounds time_range_ms = case time_range do :last_hour -> 60 * 60 * 1000 :last_day -> 24 * 60 * 60 * 1000 :last_week -> 7 * 24 * 60 * 60 * 1000 end start_time = current_time - time_range_ms # Extract entropy history for the time range entropy_history_data = state.entropy_history |> :queue.to_list() |> Enum.filter(fn {time, _entropy} -> time >= start_time end) # Calculate analytics metrics %{ time_range: time_range, data_points: length(entropy_history_data), entropy_trend: if(length(entropy_history_data) > 1, do: determine_entropy_trend_from_data(entropy_history_data), else: :insufficient_data), average_entropy: calculate_average_entropy(entropy_history_data), entropy_variance: calculate_entropy_variance(entropy_history_data), stability_score: calculate_stability_score(entropy_history_data), prediction: generate_entropy_prediction(entropy_history_data), performance_regression: detect_performance_regression(entropy_history_data), recommendations: generate_optimization_recommendations(state, entropy_history_data), maxwell_demon_stats: if(state.maxwell_demon, do: state.maxwell_demon, else: %{disabled: true}), last_updated: current_time } end defp determine_entropy_trend_from_data(entropy_data) do # Determine long-term entropy trend from historical data entropies = Enum.map(entropy_data, fn {_time, entropy} -> entropy end) slope = calculate_simple_slope(entropies) cond do slope > 0.02 -> :increasing slope < -0.02 -> :decreasing true -> :stable end end defp calculate_average_entropy(entropy_data) do case entropy_data do [] -> 0.0 data -> entropies = Enum.map(data, fn {_time, entropy} -> entropy end) Enum.sum(entropies) / length(entropies) end end defp calculate_entropy_variance(entropy_data) do case entropy_data do [] -> 0.0 data -> entropies = Enum.map(data, fn {_time, entropy} -> entropy end) mean = Enum.sum(entropies) / length(entropies) variance = entropies |> Enum.map(fn entropy -> (entropy - mean) * (entropy - mean) end) |> Enum.sum() |> Kernel./(length(entropies)) variance end end defp calculate_stability_score(entropy_data) do # Calculate system stability score (0.0 = unstable, 1.0 = perfectly stable) case entropy_data do [] -> 0.5 # Neutral score without data data -> variance = calculate_entropy_variance(data) max_variance = 1.0 # Assumed maximum variance # Lower variance = higher stability stability = 1.0 - min(variance / max_variance, 1.0) max(0.0, stability) end end defp generate_entropy_prediction(entropy_data) do case length(entropy_data) do n when n < 5 -> %{prediction: :insufficient_data} _ -> # Simple linear prediction based on recent trend recent_entropies = entropy_data |> Enum.take(-10) # Last 10 measurements |> Enum.map(fn {_time, entropy} -> entropy end) slope = calculate_simple_slope(recent_entropies) current_entropy = List.last(recent_entropies) # Predict entropy in next hour (assuming 5-second intervals) prediction_steps = 720 # 1 hour / 5 seconds predicted_entropy = current_entropy + (slope * prediction_steps) rebalancing_threshold = CosmicConstants.entropy_rebalance_threshold() time_until_rebalancing = if slope > 0 and current_entropy < rebalancing_threshold do steps_to_threshold = (rebalancing_threshold - current_entropy) / slope steps_to_threshold * 5000 # Convert to milliseconds (5-second intervals) else :not_applicable end %{ predicted_entropy: predicted_entropy, confidence: calculate_prediction_confidence(recent_entropies), time_until_rebalancing: time_until_rebalancing, trend_direction: if(slope > 0.01, do: :increasing, else: if(slope < -0.01, do: :decreasing, else: :stable)) } end end defp calculate_prediction_confidence(entropies) do # Calculate prediction confidence based on data consistency variance = entropies |> calculate_simple_variance() # Lower variance = higher confidence max(0.1, 1.0 - (variance * 2.0)) # Ensure minimum 10% confidence end defp calculate_simple_variance(values) do case values do [] -> 1.0 [_single] -> 0.0 _ -> mean = Enum.sum(values) / length(values) values |> Enum.map(fn value -> (value - mean) * (value - mean) end) |> Enum.sum() |> Kernel./(length(values)) end end defp detect_performance_regression(entropy_data) do # Detect if there's a performance regression based on entropy trends case length(entropy_data) do n when n < 10 -> %{regression_detected: false, reason: :insufficient_data} _ -> # Compare recent vs historical entropy levels {recent, historical} = Enum.split(entropy_data, -5) recent_avg = calculate_average_entropy(recent) historical_avg = calculate_average_entropy(historical) regression_threshold = 0.3 # 30% increase in entropy if recent_avg > historical_avg * (1 + regression_threshold) do %{ regression_detected: true, severity: :high, entropy_increase: recent_avg - historical_avg, percentage_increase: (recent_avg - historical_avg) / historical_avg * 100 } else %{regression_detected: false} end end end defp generate_optimization_recommendations(state, entropy_data) do # Generate intelligent optimization recommendations current_entropy = if length(entropy_data) > 0 do {_time, entropy} = List.last(entropy_data) entropy else 0.0 end recommendations = [] # High entropy recommendation recommendations = if current_entropy > CosmicConstants.entropy_rebalance_threshold() do ["Consider triggering thermodynamic rebalancing to reduce system entropy" | recommendations] else recommendations end # Maxwell's demon recommendation recommendations = if is_nil(state.maxwell_demon) do ["Enable Maxwell's demon for intelligent entropy optimization" | recommendations] else recommendations end # Vacuum stability recommendation recommendations = if not is_nil(state.vacuum_monitor) and state.vacuum_monitor.stability_metric < 0.8 do ["Monitor vacuum stability closely - instability detected" | recommendations] else recommendations end # Data distribution recommendation variance = calculate_entropy_variance(entropy_data) recommendations = if variance > 0.5 do ["High entropy variance detected - consider more frequent monitoring" | recommendations] else recommendations end case recommendations do [] -> ["System entropy is within optimal parameters"] _ -> recommendations end end defp handle_vacuum_instability(state, severity) do # Handle vacuum instability based on severity level updated_vacuum_monitor = if state.vacuum_monitor do %{state.vacuum_monitor | stability_metric: max(0.0, state.vacuum_monitor.stability_metric - (severity * 0.1)), false_vacuum_probability: min(1.0, state.vacuum_monitor.false_vacuum_probability + (severity * 0.05)) } else state.vacuum_monitor end # Update entropy state if instability is severe new_entropy_state = case severity do level when level > 0.8 -> :critical level when level > 0.5 -> :chaotic _ -> state.entropy_state end %{state | vacuum_monitor: updated_vacuum_monitor, entropy_state: new_entropy_state } end defp process_entropy_alert(state, alert_type, details) do # Process various types of entropy alerts case alert_type do :high_entropy -> # Handle high entropy alert Logger.info("📈 Processing high entropy alert: #{inspect(details)}") :vacuum_instability -> # Handle vacuum instability handle_vacuum_instability(state, details.severity) :rebalancing_needed -> # Automatically trigger rebalancing if Maxwell's demon is enabled if state.maxwell_demon and should_trigger_automatic_rebalancing(state) do trigger_maxwell_demon_optimization(state) else state end _ -> Logger.debug("🔍 Unknown entropy alert type: #{alert_type}") state end end defp entropy_persistence_loop(monitor_id) do # Background process for persisting entropy data receive do {:persist_entropy_data, timestamp, entropy_metrics} -> persist_entropy_to_filesystem(monitor_id, timestamp, entropy_metrics) {:persist_analytics, analytics_data} -> persist_analytics_to_filesystem(monitor_id, analytics_data) {:shutdown} -> Logger.info("🛑 Shutting down entropy persistence coordinator for #{monitor_id}") :shutdown after 30_000 -> :timeout # 30-second timeout end entropy_persistence_loop(monitor_id) end defp persist_entropy_to_filesystem(monitor_id, timestamp, entropy_metrics) do # Persist entropy data to time-series files try do entropy_dir = Path.join([CosmicPersistence.data_root(), "entropy", to_string(monitor_id), "time_series"]) # Create daily entropy file date = DateTime.from_unix!(div(timestamp, 1000)) date_string = Calendar.strftime(date, "%Y-%m-%d") entropy_file = Path.join(entropy_dir, "entropy_#{date_string}.json") # Append entropy data entropy_entry = %{ timestamp: timestamp, shannon_entropy: entropy_metrics.shannon_entropy, thermodynamic_entropy: entropy_metrics.thermodynamic_entropy, total_entropy: entropy_metrics.total_entropy, entropy_trend: entropy_metrics.entropy_trend, system_temperature: entropy_metrics.system_temperature, disorder_index: entropy_metrics.disorder_index, stability_metric: entropy_metrics.stability_metric } # Read existing data or create new file existing_data = if File.exists?(entropy_file) do entropy_file |> File.read!() |> Jason.decode!() else [] end # Append new data and write back updated_data = existing_data ++ [entropy_entry] entropy_file |> File.write!(safe_encode_json(updated_data)) rescue error -> Logger.warning("❌ Failed to persist entropy data: #{inspect(error)}") end end defp persist_analytics_to_filesystem(monitor_id, analytics_data) do # Persist analytics data to filesystem try do analytics_dir = Path.join([CosmicPersistence.data_root(), "entropy", to_string(monitor_id), "analytics"]) timestamp = :os.system_time(:millisecond) analytics_file = Path.join(analytics_dir, "analytics_#{timestamp}.json") analytics_file |> File.write!(safe_encode_json(analytics_data)) rescue error -> Logger.warning("❌ Failed to persist analytics data: #{inspect(error)}") end end # Safe JSON encoding without Jason dependency defp safe_encode_json(data) do try do Jason.encode!(data, pretty: true) rescue UndefinedFunctionError -> # Fallback to readable Elixir format inspect(data, pretty: true, limit: :infinity, printable_limit: :infinity) end end end