Within-Scale Thermodynamics of Thermal Turbines

This manuscript presents a Boltzmann-literal reformulation of thermodynamics in which entropy is treated as a real macroscopic physical body that stores and mediates energy. Caloric potential (CP) and mechanical potential (MP) are defined as stored thermal and mechanical energies within an entropic body, while heat (Q) and work (W) are energies emitted to the surroundings. Within this framework, three canonical relations are made explicit: a state relation defining the thermal body (TS=CP+MPTS=CP+MP), a conservation law distinguishing stored and emitted energies (CP−MP=W+QCP−MP=W+Q), and a directional admissibility law (TΔS=ΔCP−ΔMP≥0TΔS=ΔCP−ΔMP≥0) that defines irreversibility. The familiar Gibbs free energy is shown to be a microscopic projection of directional bias rather than a containment relation. Applied to thermal ratchets, molecular motors, and muscle contraction, this formulation identifies the force–velocity relationship as a direct expression of the First Law and resolves longstanding ambiguities surrounding entropy, irreversibility, and the Gibbs paradox. The work provides a unified macroscopic account of energy transduction across physical and biological systems.