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Operational quantum stochastic thermodynamics is a recently proposed theory to study the thermodynamics of open systems based on the rigorous notion of a quantum stochastic process or quantum causal model. In there, a stochastic trajectory…
The concept of work is studied in quantum thermostatistics of a system surrounded by an environment and driven by an external force. It is found that there emerges the gauge theoretical structure in a nonequilibrium process, the field of…
$\mathcal{PT}$-symmetric quantum mechanics has been considered an important theoretical framework for understanding physical phenomena in $\mathcal{PT}$-symmetric systems, with a number of $\mathcal{PT}$-symmetry related applications. This…
Quantum thermodynamics is an emerging research field aiming to extend standard thermodynamics and non-equilibrium statistical physics to ensembles of sizes well below the thermodynamic limit, in non-equilibrium situations, and with the full…
In this tutorial, we present the definition, interpretation and properties of some of the main quasiprobabilities that can describe the statistics of measurement outcomes evaluated at two or more times. Such statistics incorporate the…
We study the statistics of work, dissipation, and entropy production of a quantum quasi-isothermal process, where the system remains close to the thermal equilibrium along the transformation. We derive a general analytic expression for the…
Although the laws of classical physics are deterministic, thermodynamics gives rise to an arrow of time through irreversible processes. In quantum mechanics the unitary nature of the time evolution makes it intrinsically reversible, however…
This article sets up a new formalism to investigate stochastic thermodynamics of out-of-equilibrium quantum systems, where stochasticity primarily comes from quantum measurement. In the absence of any bath, we define a purely quantum…
Time-asymmetric behavior as embodied in the second law of thermodynamics is observed in {\it individual macroscopic} systems. It can be understood as arising naturally from time-symmetric microscopic laws when account is taken of a) the…
The thermodynamic behavior of out-of-equilibrium quantum systems in finite-time dynamics encompasses the description of energy fluctuations, which dictates a series of system's physical properties. In addition, strong interactions in…
Work in closed quantum systems is usually defined by a two-point measurement. This definition of work is compatible with quantum fluctuation theorems but it fundamentally differs from its classical counterpart. In this paper, we study the…
The classical Jarzynski equality establishes an exact relation between the stochastic work performed on a system driven out of thermal equilibrium and the free energy difference in a corresponding quasi-static process. This fluctuation…
We study the physics of quantum phase transitions from the perspective of non-equilibrium thermodynamics. For first order quantum phase transitions, we find that the average work done per quench in crossing the critical point is…
Microscopic physical laws are time-symmetric, hence, a priori there exists no preferential temporal direction. However, the second law of thermodynamics allows one to associate the "forward" temporal direction to a positive variation of the…
There are both practical and foundational motivations to consider the thermodynamics of quantum systems at small scales. Here we address the issue of autonomous quantum thermal machines that are tailored to achieve some specific…
Understanding thermodynamics far from equilibrium at the quantum scale remains a fundamental challenge, particularly in the presence of quantum coherence. Here we develop a first-principles framework for nonequilibrium quantum…
The symmetry of quantum theory under time reversal has long been a subject of controversy because the transition probabilities given by Born's rule do not apply backward in time. Here, we resolve this problem within a rigorous operational…
We formulate a geometric framework in which physical laws emerge from restricted access to microscopic information. Measurement constraints are modeled as a gauge symmetry acting on density operators, inducing a gauge-reduced space of…
We discuss the thermodynamics of closed quantum systems driven out of equilibrium by a change in a control parameter and undergoing a unitary process. We compare the work actually done on the system with the one that would be performed…
The aim of this book chapter is to indicate how quantum phenomena are affecting the operation of microscopic thermal machines, such as engines and refrigerators. As converting heat to work is one of the fundamental concerns in…