which play important roles in quantitative understanding of the experimental data [@Wang:2016opj].

The theoretical framework of relativistic dissipative hydrodynamics, however, is still not completely understood, partially because one has to introduce relaxation effects to the off-equilibrium processes to avoid violating stability and causality [@Hiscock:1983zz; @Hiscock:1985zz; @Hiscock:1987zz]. Such extended frameworks are called the second-order theory [@Israel:1976tn; @Israel:1979wp; @Muronga:2001zk; @Muronga:2003ta; @Muronga:2006zw; @Muronga:2006zx; @Koide:2006ef; @Tsumura:2006hn; @Tsumura:2007wu; @Tsumura:2009vm; @Tsumura:2011cj; @Tsumura:2012ss; @Baier:2007ix; @Romatschke:2009kr; @Bhattacharyya:2008jc; @Natsuume:2007ty; @Lublinsky:2009kv; @Betz:2009zz; @Monnai:2010qp; @Monnai:2018rgs; @Molnar:2013lta; @Denicol:2012cn; @Denicol:2012vq; @Denicol:2019iyh; @PeraltaRamos:2009kg; @Calzetta:2010au; @Aguilar:2017ios; @Florkowski:2015lra; @Jaiswal:2015mxa; @Tinti:2016bav; @Harutyunyan:2018cmm; @Mitra:2019jld] as opposed to the traditional linear response theory [@Landau; @Eckart:1940te], which is also known as the first-order theory, because the off-equilibrium correction of the respective order in terms of dissipative currents is taken into account in the entropy current of those theories.

Non-relativistic hydrodynamic flow can be defined as a local flux of particles. In relativistic systems, however, the definition of the flow is not trivial because the energy and the conserved number can flow separately in the presence of dissipative processes. There are two distinctive ways of defining the local rest frame for the flow: the Landau (or energy) frame [@Landau] and the Eckart (or conserved charge/particle) frame [@Eckart:1940te]. There have been decades 