In thermodynamics, Clausius entropy is a term used, in various publications, to differentiate between the original 1865 formulation of entropy, by German physicist Rudolf Clausius, and other more abstract formulations. Polish physicist Michal Kurzynski outlines one take on this view as such: [1]

“The function S was introduced into thermodynamics at the phenomenological level by Clausius in 1865, and we this call it the Clausius entropy, in contrast to the statistical Boltzmann-Gibbs entropy, being in general only a function of the probability density.”

Many non standard variants of entropy, such as Shannon entropy, Hartley entropy, or Teachman-Shannon entropy, among others exotics, exist, many having nothing to do with thermodynamics, yet are often named as such to make an indirect claim to have something to do with universal laws.

References
1. Kurzynski, Michal. (2006). The Thermodynamic Machinery of Life (pg. 40). New York: Springer.

Further reading
● Medvedeva, M.L. (1995). “Thermomechanical Tnterpretation of Clausius Entropy.” (abstract) Chemical and Petroleum Engineering, Vol. 31, No. 10. Oct.
● Eu, Byung C. (2002). Generalized Thermodynamics (section: Clausius Entropy for Reversible Processes, pgs. 45-46). Springer.