Figure 1.

Scheme of the formal approach to expressions (1)–(4). (a) A time-discretization is implemented in order to characterize the microscopical reversibility condition; (b) A qualitative scheme of possible trajectories between macrostates on the global phase space. The macroscopic coarse-grained states, $\mathcal{A}$ (dark shaded region) and $\mathcal{B}$ (light shaded region) are defined as disjoint ($\mathcal{A}\cap \mathcal{B}=\varnothing$) sections on the phase state $\mathsf{\Omega }$. The set of forward paths of duration $\tau$ constrained to start in $\mathcal{A}$ and finish in $\mathcal{B}$ is denoted by ${\mathbf{x}}_{\tau }$.