Correction: Entropy flow in thermoelectric/thermochemical transport(MRS Bulletin, 10.1557/s43577-024-00746-1)

This article was updated to make the following changes in the text. “Thermoelectric” was changed to “thermoelectric material” above Equation 4. r=-1/2 should be in regular text rather than being in superscript, (i.e., should be For acoustic deformation scattering¹, r=-1/2) above Equation 8. In Equation 11, c_v(T,v) was deleted. (i.e., S_e=c_v(T,v)=π²2k_BTT_f changed to S_e=π²2k_BTT_f) Below Equation 12, “Is the Seebeck coefficient a scalar or second-rank tensor?” should be normal text rather than being italic. Below Equation 43, “Onsager reciprocity relation” should be normal text rather than being italic. Below Equation 44, “Onsager coefficients in entropic representation” should be normal text rather than being italic. Equation 37: φ˙=-∇T·J→_s=-∇T·(J→_s+s_iJ→_i)=-∇T·J→_s-(s_i∇T)·J→_i, where J→_s is the entropy flux density purely due to heat conduction driven by the temperature gradient ∇Tshould be: φ˙=-∇T·J→_s=-∇T·(J→_S,h+s_iJ→_i)=-∇T·J→_S,h-(s_i∇T)·J→_i, where J→_S,h is the entropy flux density purely due to heat conduction driven by the temperature gradient ∇T Above Equation 45, “The heat flux density purely due to a chemical potential gradient under a uniform temperature” changed to “The thermal energy flux density purely due to a chemical potential gradient under a uniform temperature.” Equation 45 J→_Q=-L_Qi∇μ_i=TJ→_s=Ts_iJ→_i=Ts_i(-n_iM_i∇μ_i)=-T²s_in_iM_i∇μ_iTchanged to J→_Q=-L_Qi∇μ_iT=TJ→_s=Ts_iJ→_i=Ts_i(-n_iM_i∇μ_i)=-T²s_in_iM_i∇μ_iT “Thermoelectric” was changed to “thermoelectric material” above Equation 4. r=-1/2 should be in regular text rather than being in superscript, (i.e., should be For acoustic deformation scattering¹, r=-1/2) above Equation 8. In Equation 11, c_v(T,v) was deleted. (i.e., S_e=c_v(T,v)=π²2k_BTT_f changed to S_e=π²2k_BTT_f) Below Equation 12, “Is the Seebeck coefficient a scalar or second-rank tensor?” should be normal text rather than being italic. Below Equation 43, “Onsager reciprocity relation” should be normal text rather than being italic. Below Equation 44, “Onsager coefficients in entropic representation” should be normal text rather than being italic. Equation 37: φ˙=-∇T·J→_s=-∇T·(J→_s+s_iJ→_i)=-∇T·J→_s-(s_i∇T)·J→_i, where J→_s is the entropy flux density purely due to heat conduction driven by the temperature gradient ∇T should be: φ˙=-∇T·J→_s=-∇T·(J→_S,h+s_iJ→_i)=-∇T·J→_S,h-(s_i∇T)·J→_i, where J→_S,h is the entropy flux density purely due to heat conduction driven by the temperature gradient ∇T Above Equation 45, “The heat flux density purely due to a chemical potential gradient under a uniform temperature” changed to “The thermal energy flux density purely due to a chemical potential gradient under a uniform temperature.”