arXiv subjects
Publications and source records attributed to Jang-il Sohn.
In the present work, we study the entropy productions in a system controlled by double control parameters. By introducing a thermal fluctuation part, we solve the problem that the second law of the thermodynamics seems to be violated by the thermal fluctuation near equilibrium in the microscopic levels. Then we define the negative and the compensating entropy productions in the macroscopic levels.
In statistical physics, entropy is generally logarithm of probability. Therefore, if dynamics is decomposed by log, entropy production should be decomposed properly. In the present work, log-decomposition of dynamics is introduced. By which time evolution operator is logarithmically decomposed into a symmetric operator and an asymmetric factor. Path probability and path entropy production are also systematically and intuitively decomposed into symmetric and asymmetric parts. From symmetric operator, non-adiabatic entropy production is derived, whereas adiabatic entropy production is from asymmetric factor.
By applying adiabatic theorem to a Markovian system, we calculate the adiabatic and diabatic entropy changes along a path. As well known, the total path entropy change is separated into two parts, system and environment entropy changes, $ΔS_{tot} = ΔS_{sys} + ΔS_{env}$. The environment entropy change, $ΔS_{env}$, is divided again into two parts, an adiabatic contribution due to work, $ΔS_{\mathcal{W}}$, and a diabatic contributions due to heat, $ΔS_{\mathcal{Q}}$. In an adiabatic process, total path entropy change is same with the adiabatic path entropy change, $ΔS_{A}$, which is given by sum of system entropy change and adiabatic contribution, $ΔS_{A} = ΔS_{sys} + ΔS_{\mathcal{W}}$. Mathematical form of $ΔS_{A}$ is a type of excess heat entropy change, but $ΔS_{A}$ is due to work. By which, it is shown that the terms adiabatic and non-adiabatic contributions of $ΔS_{na}$ and $ΔS_{a}$ in [Phys. Rev. Lett. {\bf 104}, 090601 (2010)] should be completely switched, $i.e.$ $ΔS_{na} \rightarrow ΔS_{A}$ and $ΔS_{a} \rightarrow ΔS_{\mathcal{Q}}$ in fact.