Consistent thermodynamic framework for interacting particles by neglecting thermal noise

An effective temperature theta, conjugated to a generalized entropy s(q), was introduced recently for a system of interacting particles. Since theta presents values much higher than those of typical room temperatures T << theta the thermal noise can be neglected (T/theta similar or equal to 0) in these systems. Moreover, the consistency of this definition, as well as of a form analogous to the first law of thermodynamics, du = theta ds(q) + delta W, were verified lately by means of a Carnot cycle, whose efficiency was shown to present the usual form, eta = 1 - (theta(2)/theta(1)). Herein we explore further the heat contribution delta Q = theta ds(q) by proposing a way for a heat exchange between two such systems, as well as its associated thermal equilibrium. As a consequence, the zeroth principle is also established. Moreover, we consolidate the first-law proposal by following the usual procedure for obtaining different potentials, i.e., applying Legendre transformations for distinct pairs of independent variables. From these potentials we derive the equation of state, Maxwell relations, and define response functions. All results presented are shown to be consistent with those of standard thermodynamics for T > 0.