Thermodynamics of Cooperation: Thermodynamic Friction

We quantify the energy cost of adversarial resource competition between self-maintaining open thermodynamic systems. Boundary constraints are required for multi-agent resource allocation; we model what happens when those constraints are violated. Using Tullock contest theory and a boundary-integrity damage model, we prove that unconstrained conflict is a net-negative thermodynamic outcome: under realistic physical parameters, the total energy dissipated by conflict, including contest expenditure, boundary damage, and thermodynamically irreversible repair costs, exceeds the value of the contested resource. We derive explicit Nash equilibrium investments and damage functions for both symmetric and asymmetric contests, showing that contest dissipation approaches the full resource value as the number of contestants grows. Extending the analysis to cooperative networks, we prove that a single constraint violation cascades through the network, with illustrative amplification ratios on the order of $10^3$ to $10^4$ under modest network parameters, because trust recovery is gradual while trust destruction is instantaneous. Cooperation strictly dominates conflict for all physically realizable friction parameters, providing the energy-denominated cost structure that enters the game-theoretic payoff matrices of the subsequent paper in this series.