Stochastic entropy production, which quantifies the difference between the probabilities of trajectories of a stochastic dynamics and its time reversals, has a central role in nonequilibrium thermodynamics. In the theory of probability, the change in the statistical properties of observables due to reversals can be represented by a change in the probability measure. We consider operators on the space of probability measure that induce changes in the statistical properties of a process, and formulate entropy productions in terms of these change-of-probability-measure (CPM) operators. This mathematical underpinning of the origin of entropy productions allows us to achieve an organization of various forms of fluctuation relations: All entropy productions have a non-negative mean value, admit the integral fluctuation theorem, and satisfy a rather general fluctuation relation. Other results such as the transient fluctuation theorem and detailed fluctuation theorems then are derived from the general fluctuation relation with more constraints on the operator of a entropy production. We use a discrete-time, discrete-state-space Markov process to draw the contradistinction among three reversals of a process: time reversal, protocol reversal and the dual process. The properties of their corresponding CPM operators are examined, and the domains of validity of various fluctuation relations for entropy productions in physics and chemistry are revealed. We also show that our CPM operator formalism can help us rather easily extend other fluctuations relations for excess work and heat, discuss the martingale properties of entropy productions, and derive the stochastic integral formulas for entropy productions in constant-noise diffusion process with Girsanov theorem. Our formalism provides a general and concise way to study the properties of entropy-related quantities in stochastic thermodynamics and information theory. *

Due to their unique longevity and capacity to secrete high levels of protein, plasma B cells have the potential to be used as a cell therapy for protein replacement. Here, we show that ex vivo engineered human plasma cells exhibit single-cell RNA profiles, scanning electron micrograph ultrastructural features, and in vivo homing capacity of long-lived plasma cells. After transferring human plasma cells to immunodeficient mice in the presence of the human cytokines BAFF and IL-6, we observe increases in retention of plasma cells in the bone marrow, with engraftment exceeding a year. The most profound in vivo effects of human IL-6 are observed within 20 days of transfer and could be explained by decreased apoptosis in newly differentiated plasma cells. Collectively, these results show that ex vivo engineered and differentiated human plasma cells have the potential for long-lived in vivo protein secretion, which can be modeled in small animals.