It is a central question in quantum thermodynamics to determine how irreversible is a process that transforms an initial state $\ensuremath{\rho}$ to a final state $\ensuremath{\sigma}$ and whether such irreversibility can be thought of as a useful resource. For example, we might ask how much work can be obtained by thermalizing $\ensuremath{\rho}$ to a thermal state $\ensuremath{\sigma}$ at temperature $T$ of an ambient heat bath. Here, we show that, for different sets of resource-theoretic thermodynamic operations, the amount of entropy produced along a transition is characterized by how reversible the process is. More specifically, this entropy production depends on how well we can return the state $\ensuremath{\sigma}$ to its original form $\ensuremath{\rho}$ without investing any work. At the same time, the entropy production can be linked to the work that can be extracted along a given transition and we explore the consequences that this fact has for our results. We also exhibit an explicit reversal operation in terms of the Petz recovery channel coming from quantum information theory. Our result establishes a quantitative link between the reversibility of thermodynamical processes and the corresponding work gain.It is a central question in quantum thermodynamics to determine how irreversible is a process that transforms an initial state $\ensuremath{\rho}$ to a final state $\ensuremath{\sigma}$ and whether such irreversibility can be thought of as a useful resource. For example, we might ask how much work can be obtained by thermalizing $\ensuremath{\rho}$ to a thermal state $\ensuremath{\sigma}$ at temperature $T$ of an ambient heat bath. Here, we show that, for different sets of resource-theoretic thermodynamic operations, the amount of entropy produced along a transition is characterized by how reversible the process is. More specifically, this entropy production depends on how well we can return the state $\ensuremath{\sigma}$ to its original form $\ensuremath{\rho}$ without investing any work. At the same time, the entropy production can be linked to the work that can be extracted along a given transition and we explore the consequences that this fact has for our results. We also exhibit an explicit reversal operation in terms of the Petz recovery channel coming from quantum information theory. Our result establishes a quantitative link between the reversibility of thermodynamical processes and the corresponding work gain.

arXiv:1506.08145Physical Review AJun 15, 201827 citations

How isolated is enough for an "isolated" system in statistical mechanics?

Hui Liang Dong, Da‐Wei Wang, M.B. Kim

Irreversible processes are frequently adopted to account for the entropy increase in classical thermodynamics. However, the corresponding physical origins are not always clear, e.g. in a free expansion process, a typical model in textbooks. In this letter, we study the entropy change during free expansion for a particle with the thermal de Broglie wavelength ( $λ_{T}$ ) in a one-dimensional square trap with size $L$ . By solely including quantum dephasing as an irreversible process, we recover classical result of entropy increase in the classical region ( $L\ggλ_{T}$ ), while predict prominent discrepancies in the quantum region ( $L\llλ_{T}$ ) because of non-equilibrium feature of trapped atoms after expansion. It is interesting to notice that the dephasing, though absent in classical system, is critical to clarify mysteries in classical thermodynamics.Irreversible processes are frequently adopted to account for the entropy increase in classical thermodynamics. However, the corresponding physical origins are not always clear, e.g. in a free expansion process, a typical model in textbooks. In this letter, we study the entropy change during free expansion for a particle with the thermal de Broglie wavelength ($λ_{T}$) in a one-dimensional square trap with size $L$. By solely including quantum dephasing as an irreversible process, we recover classical result of entropy increase in the classical region ($L\ggλ_{T}$), while predict prominent discrepancies in the quantum region ($L\llλ_{T}$) because of non-equilibrium feature of trapped atoms after expansion. It is interesting to notice that the dephasing, though absent in classical system, is critical to clarify mysteries in classical thermodynamics.

arXiv:1706.02636Jun 8, 20172 citations

T

of an ambient heat bath. Here, we show that, for different sets of resource-theoretic thermodynamic operations, the amount of entropy produced along a transition is characterized by how reversible the process is. More specifically, this entropy production depends on how well we can return the state $\ensuremath{\sigma}$ to its original form $\ensuremath{\rho}$ without investing any work. At the same time, the entropy production can be linked to the work that can be extracted along a given transition and we explore the consequences that this fact has for our results. We also exhibit an explicit reversal operation in terms of the Petz recovery channel coming from quantum information theory. Our result establishes a quantitative link between the reversibility of thermodynamical processes and the corresponding work gain.

λ_{T}

) in a one-dimensional square trap with size

L

. By solely including quantum dephasing as an irreversible process, we recover classical result of entropy increase in the classical region (

L\ggλ_{T}

), while predict prominent discrepancies in the quantum region (

L\llλ_{T}

) because of non-equilibrium feature of trapped atoms after expansion. It is interesting to notice that the dephasing, though absent in classical system, is critical to clarify mysteries in classical thermodynamics.