t = 0.000 

  

    Two-chamber + channel + piston heat engine. The LEFT chamber is
    thermally coupled to a T_hot bath (the heat source), the
    RIGHT chamber to a T_cold bath (the heat sink). The channel
    between them is where the throttling dissipation D lives. The piston on
    the far right extracts (or supplies) work. The cycle runs:
    compress (push gas from R to L through the channel) →
    hold-hot (gas in L absorbs Q_hot from T_hot bath) →
    expand (hot gas jets back through channel and pushes piston out,
    delivering work) → hold-cold (gas in R rejects Q_cold to T_cold
    bath). The 2nd-Law witness: η_engine = W_net/Q_hot stays below the Carnot
    bound 1 − T_c/T_h by an amount controlled by D, which is dominated by the
    turbulent dissipation in the jet through the channel.