Thermodynamic interpretation of generalized entropies

Determine whether, for maximum-entropy distributions obtained from a generalized entropy functional S under an energy constraint, the associated Lagrange multiplier can be interpreted as the inverse physical temperature, and ascertain whether there exists any physical system for which the extremal value S[p_i^{*}] is related to Clausius’s thermodynamic entropy defined via heat flow.

Background

In classical thermodynamics using the Boltzmann–Gibbs–Shannon entropy, the Lagrange multiplier enforcing the average-energy constraint is interpreted as the inverse temperature. The paper questions whether this identification extends to generalized entropies emerging from the group-entropic framework.

The authors emphasize that, although one can compute extremal distributions p_i^{*} and the corresponding values S[p_i^{*}] for any generalized entropy, it is unknown if these have a precise thermodynamic meaning in relation to Clausius’s entropy for real physical systems.