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The origins of thermodynamics from the microscopic properties of matter havenot been satisfactorily accounted for. This work presents a formulation thatconnects Lagrangian mechanics to thermodynamics. By using such a formulationand following similar steps to those performed in the laboratory, the heatcapacities, energetic and mechanical response coefficients, absorbed andemitted heats, entropy changes, and thermodynamic energies of a prototype watersystem, employed as an illustrative example, are found to be close to theexperimental results on water bulk. The present formulation is realistic. Afterconnecting Lagrangian mechanics to Langevin stochastic dynamics, the first lawof thermodynamics is derived. The formulation not only exhibits thetransformation of time-reversible equations onto time-irreversible equations,and the molecular origins of heat as well, but also reveals new pathways toinvestigate the thermodynamics of systems of nanometric sizes.

Molecular Nature of Thermodynamics and its Application to Nanosize Particle Systems