There are many functional contexts where it is desirable to maintain a mesoscopic system in a nonequilibrium state. However, such control requires an inherent energy dissipation. In this article, we unify and extend a number of works on the minimum energetic cost to maintain a mesoscopic system in a prescribed nonequilibrium distribution using ancillary control. For a variety of control mechanisms, we find that the minimum amount of energy dissipation necessary can be cast as an information-theoretic measure of distinguishability between the target nonequilibrium state and the underlying equilibrium distribution. This work offers quantitative insight into the intuitive idea that more energy is needed to maintain a system farther from equilibrium.
We determine the minimum energy required to control the evolution of any mesoscopic quantum system in the presence of arbitrary Markovian noise processes. This result provides the mesoscopic equivalent of the fundamental cost of refrigeration, sets the minimum power consumption of mesoscopic devices that operate out of equilibrium, and allows one to calculate the efficiency of any control protocol, whether it be open-loop or feedback control. As examples, we calculate the energy cost of maintaining a qubit in the ground state and the efficiency of resolved-sideband cooling of nano-mechanical resonators, and discuss the energy cost of quantum information processing.
Recent developments of the analysis of the second law of thermodynamics by using the information theoretic quantities has led to the discovery of the so-called nonequilibrium free energy and has allowed us to formulate thermodynamic relations for arbitrary nonequilibrium initial and final states.By using the nonequilibrium free energies, we can quantify thermodynamic costs of information encoding and erasure processes as well as to quantify the extractable work from information heat engines in a unified way.In those general situations, reducing dissipation allows us to increase the extractable work from the system (or to reduce the work cost), and reducing work fluctuation allows us to narrow the work probability distribution and to extract a fluctuation-free work from the system.Suppressing both work fluctuation and dissipation as much as possible is vital to control mesoscopic and nano systems that work at the level of thermal fluctuations.Previous studies have searched for a vanishing work fluctuation protocol by using techniques of quantum information theory, known as the single-shot statistical mechanics (and sometimes called the deterministic work extraction protocol) and the vanishing dissipation protocol, known as the thermodynamically reversible protocol by using the second law of thermodynamics.In this thesis, we address issues concerning a method to control nonequilibrium systems by using fluctuation theorems and trade-off relation between work fluctuation and fluctuation in dissipation.We derive quantum fluctuation theorems under measurement and feedback control, which allow us to study how to suppress dissipation during a general quantum measurement and a feedback control.We then consider a method to suppress work fluctuation and fluctuation in dissipation simultaneously as much as possible by showing the trade-off relation between work and dissipation in terms of their standard deviations and derive an explicit protocol that achieves the lower bound of the trade-off relation.We show that the explicit protocol reproduces the deterministic work extraction protocol in the limit of vanishing work fluctuation and the thermodynamically reversible protocol in the limit of vanishing fluctuation in dissipation.
We establish the fluctuation theorem in the presence of information exchange between a nonequilibrium system and other degrees of freedom such as an observer and a feedback controller, where the amount of information exchange is added to the entropy production. The resulting generalized second law sets the fundamental limit of energy dissipation and energy cost during the information exchange. Our results apply not only to feedback-controlled processes but also to a much broader class of information exchanges, and provide a unified framework of nonequilibrium thermodynamics of measurement and feedback control.
Observer-information entropy production quantifies the loss of recoverable information about a physical source when an already formed observation undergoes source-independent irreversible degradation. The statistical second-law statement
Σobs[s,t]=I(X;Rs)−I(X;Rt)=I(X;Rs∣Rt)≥0 follows from data processing, but by itself it does not identify a physical energetic or thermodynamic cost. This paper establishes such a connection within an explicit and deliberately restricted stochastic-thermodynamic regime. We consider a finite observer memory
Rt coupled to a single heat bath at temperature
T. A source label
X is fixed during the passive relaxation, the transition generator of
Rt is independent of
X, and the memory dynamics satisfies detailed balance with respect to a strictly positive equilibrium law
q. For the joint source--memory ensemble and for the unconditioned memory marginal, we define the standard stochastic-thermodynamic entropy-production rates. Using the relative-entropy chain rule and the detailed-balance
H-theorem, we prove the exact correlation-dissipation decomposition
kBS˙totXR=σobs+kBS˙totR. Consequently,
S˙totXR≥kBσobs,ΔStotXR[s,t]≥kBΣobs[s,t]. At fixed temperature the same result is an excess-free-energy dissipation bound, \[ \Fex_{XR}(s)-\Fex_{XR}(t) \ge k_BT\Sigma_{\mathrm{obs}}[s,t]. \] Equality holds when the memory marginal remains at equilibrium, in which case all thermodynamic irreversibility is attributable to the destruction of source--record correlation. A symmetric two-state memory provides an exactly solvable saturation example. The result is not a universal Landauer principle. It constrains total entropy production and loss of nonequilibrium free energy during passive decorrelation; it does not assert a universal heat or work cost for arbitrary information loss. Driven memories, source-dependent transition rates, active measurement, feedback, multiple reservoirs, and nonequilibrium steady states require the broader information-thermodynamic bookkeeping developed in stochastic thermodynamics. We then place the thermodynamic result beside two Fisher--Shannon bridges. Under Gaussian observation heat flow
Yt=X+Bt, observer-information dissipation obeys the exact identity
σobs(t)=21(td−J(Yt))=2t21mmse(X∣Yt), while pairwise statistical distinguishability obeys \[ \frac{d}{dt}\KL(p_t\|q_t) =-\frac12\Jrel(p_t\|q_t). \] Recent temporal-Fisher speed-limit results provide a complementary route from physical entropy production to the speed of probability evolution. Together these results separate three objects that are often conflated: thermodynamic irreversibility, Shannon information loss about the physical source, and Fisher-geometric statistical motion. The paper thereby supplies a physical-cost layer for observer information theory without identifying information with energy or thermodynamic entropy.
A central open question in quantum thermodynamics is the identification of thermodynamic entropy away from equilibrium. Although thermodynamic entropy coincides with the von Neumann entropy for a Gibbs state at equilibrium, the thermodynamic role of quantum coherence generated during nonequilibrium evolution remains unclear. Here, we show that von Neumann entropy does not, in general, represent the thermodynamic entropy governing heat exchange in coherent nonequilibrium quantum systems. By integrating the resource theory of quantum coherence with thermodynamic principles, we develop a general framework for nonequilibrium quantum thermodynamics. We identify thermodynamic entropy with the energy entropy derived from energy-measurement statistics and introduce a dynamical temperature extending the equilibrium concept to nonequilibrium states. Consequently, we obtain an exact entropy-balance relation separating the entropy flux associated with heat exchange from the coherence-loss contribution to entropy production, establishing an operational connection between quantum coherence, heat flow, and total entropy change. Unlike approaches relying on equilibrium reference states or stationary Gibbs ensembles, our framework uses instantaneous dynamical quantities and remains valid throughout transient nonequilibrium evolution. It provides consistent dynamical definitions of temperature, work, heat, and free energy. Applying the formalism to an exactly solvable open quantum system, we show that the first and second laws hold throughout transient evolution and that equilibrium thermodynamics emerges dynamically in the weak-coupling long-time limit. Our results establish a unified framework for coherent nonequilibrium quantum thermodynamics and suggest opportunities for controlling heat dissipation through coherence engineering in quantum thermal technologies.