  In the paper, "Time & clocks: A thermodynamic approach" Lucia and Grisolia
describe the connections between the physical nature of time and macroscopic
irreversibility in thermodynamics. They also discuss the possibility of
constructing a thermodynamic clock that links the two, through an approach
based on the behaviour of a black body. Their work primarily focuses on the
macroscopic irreversibilty, and their attempt to define 'thermodynamic time' is
grounded on the concepts from non-equilibrium thermodynamics such as, entropy
generation and time-dependent thermodynamic fluxes - in and out of the system.
In this letter, we present a first principles approach based on the Maupertuis
principle to describe the connection between time and thermodynamics for
equilibrium phenomena. Our novel interpretation of the temperature as a
functional allows us to extend our formalism to irreversible processes when the
local equilibrium hypothesis is satisfied. Through our framework we also
establish a functional relationship between equilibrium and non-equilibrium
time-scales while distinguishing between the two.
