A dynamical field theory for dissipative thermal systems. The first and second laws of irreversible thermodynamics

Abstract

The thermodynamics of irreversible processes is derived from the principles of dynamical field theory independently of all elements of thermostatics, in particular the assumption of local equilibrium. Field thermodynamics proceeds from the premise that all driving forces experienced by the molecules in a continuum are conservative and arise from scalar potential functions. Dynamically the temperature potential T is no different from the pressure potential p. A field is converted to a force upon multiplication by a scale factor. A potential is converted to potential energy by the same scale factor. To scale the field −▿ p to the force per mole of molecular species k, the partial molar volume V¯ k is the scale factor. Similarly the partial molar entropy, S¯ k , scales the temperature field. The transition from the scale factors (which are physical parameters) to the systemic variables, for example S¯ k → s(x, y, z; t) , is not trivial. From the dynamics and the structure of the derived potential energy function are inducted the conjugate variables such as ( p, V I ) and ( T, s). The meta-mechanical properties of the thermal variables ( T, s) are discovered via the local First Law of Thermodynamics, which relates internal energy, thermal flux, and work, and from the local Second Law, which prescribes the possible partitions of internal energy between kinetic, potential, and thermal energies. From the form of the potential energy come Maxwell's relationships. From the energy partition comes the equation of continuity for entropy, with its important source term. In contrast to earlier theories of irreversible thermodynamics, the dissipation function does not include the stress tensor, a constitutive parameter.